Learn to DM: Prepping for, and running, a game.

[Charon]

I can't DM, I don't know all the rules!
Spoiler: No one does. You don't need to know all the rules. You just need to know the rules that are gonna come up next session.

Welcome to my guide on how to prep for and run a game of DnD!

Let's start by discussing the states of play. At any given time a DnD game is in a state of either exploration, social or combat. Or more simply put, looky, talky, stabby. And as the game exists in one of these states, it can then transition into one of the other two states. This means that while you can never predict what the players might do, you can at least predict where the game is going.
Sure, for the first session it's gonna be a bit unpredictable, but between sessions, you should have a really good idea of what's coming up. If you finish a session on a cliffhanger, right before the big boss fight then you know next session is opening in a state of combat and you probably have a pretty good idea of whether that's going to transition into exploration (as the PCs delve deeper into the dungeon) or social (as they return to town and hand in their quest).
If the players are deep in a dungeon they are likely to flit between exploration and combat rather than social.
If they're at the Duchess' birthday gala then it's probably social with a little bit of exploration as they sneak off to search her private rooms.
Point is, despite the unpredictability of players, the situation is predictable. If the players are sneaking around at the Duchess' party you can prepare expecting social and exploration and maybe some combat if the Duchess is evil and her guards might stop them or her werewolf bodyguard.

Once you know what to expect, you can prep for a session.

Prepping for exploration.
This is pretty easy. If you know your players are exploring then you likely know what they are exploring. Prepping for that is mostly about writing good descriptions of things they might find while exploring. If this is the dungeon, simply describe everywhere they might go within the boundaries you've set.
"A musty smell assails your nostrils as you enter this chamber. There are ragged, filth stained blankets in the corner, a dried out latrine and a small pile of what looks like animal bones in the corner. Something was sleeping here, but not recently. Whatever creature inhabited this chamber it has long since departed."
If this is more sandboxy like the Duchess' mansion, start with the most likely areas. Describe the area they sneak off to directly from the party as well as the duchess' private bedroom. Think about where else they might end up. Perhaps a description of an ornate bathroom or the library they enter after taking a wrong turn.
Visual descriptions are of course key here but don't forget to describe audible components and even smells to bring it to life. Also don't neglect describing the people that are encountered, what do they look like, what are they wearing, how do they carry themselves, how do they interact with their environment, etc... you have all the time in the world to make it good.
"You slip off from the party through the first unwatched door you find and emerge into a fancy corridor. Nearby a butler and a maid are smooching, the man's hand firmly gripping the maid's buttock. Suddenly realising they are not alone, their clandestine affair comes to a quick close as they scurry off out of sight leaving you free to explore. You see two doors in easy reach and a third that the two lovebirds escaped through. At the end of the corridor, blue carpeted stairs lead upward. Looking up, an ornate golden chandelier with crystals shaped like tears hangs high above you."
Having these little set pieces handy brings your world to life.
If this is an even wider sandbox like PCs are wandering around town then prep a handful of NPCs they might bump into and make them interesting and/or put them in interesting situations.
"You make your way to the library. As you approach the steps, the door bursts open and a blue-skinned tiefling woman and an overweight human man emerge, arguing heatedly, the woman's tail cracking like a whip to punctuate her points. The man finally relents, throws his hat angrily into the street and storms off, leaving the tiefling woman with a scowl on her face, her arms crossed and muttering under her breath as she looks up at the sky as if seeking guidance... or intervention."
The more interesting they are, the more likely the PCs are to engage with them, something that you can prep for, a state switch into social!

Prepping for social.
Most of the time you will know which NPCs are present and can prep for the fact that PCs might talk to them. You can practice a voice if you have the talent but it isn't mandatory. If you don't do voices, give them some mannerisms instead. Maybe they talk really quickly or really slowly or have a lisp? Give them motivations. Why are they here? What do they want? How can they help the PCs or the PCs help them? Or are they instead a hindrance? Are they hostile? Could this transition to a combat state? If so, have their stats to hand. Prep some lines of dialogue if you know where the conversation will go. If the PCs suspect the Duchess of trading illegally with the desert lizardfolk they might try hint at it or query her outright, so have her responses ready to go. If she's secretly a lizardfolk wearing an illusion that they might be able to dispel, then have her combat stats ready to go.

Prepping for combat.
Again, most of the time when combat breaks out, you're expecting it. Have the monster's stats to hand, either written down or at the least, a note of which page of the MM you need to be on. More than that, be prepared for the attacks the monster has. You don't need to know the grapple rules if the PCs are fighting a wolf but if you're fighting a roper then you definitely should. Don't wait til combat breaks out to be looking them up. Write them down, have a read of them before the session starts. The same goes for enemies with spells. If your bad guy's main thing is that he casts hold person then you should have that info ready to go and brush up on how it works pre session so when he casts it, you don't need to open a book, you can simply call for the appropriate saving throw and glance at a note behind your screen to check the DC. You'll find your players will be impressed and this is step one on the path to getting that mystical reputation for being a DM who knows all the rules.

Prepping for the PCs.
And just like prepping for enemy abilities, know what your PCs are capable of. If the party has a barbarian, he's gonna rage, often. Party doesn't have a monk, then you don't need to know how flurry of blows works. This is even more crucial when a player levels up. If the wizard just took Tasha's Hideous Laughter then you know he's gonna be looking for any opportunity to cast it. Don't be caught by surprise. Look it up, take notes, make a note of the save and the DC so when he casts it for the first time you can confidently say, ok, that's a will save for my orc, right, what's your DC, 15?
Oh my god, he knows every spell in the book, he didn't even have to look!
Likewise, if the fighter just got a bonus feat and took improved grapple you can bet your bottom dollar he's gonna grapple the next bad guy he comes across. Look it up, be ready.
Fighter just multiclassed into rogue? Look up sneak attacks.

It's really just common sense. Make notes on what you expect to come up, keep them behind your screen. Include a page reference in case you do need to look up a clarification in a book. There'll still be things you didn't expect, that you didn't prep for, but good prep simply minimizes those occurences.

So the pre is done, what about actually running the game?

First rule. Roll behind the screen. There's always the urge to be open and fair but that isn't your job. There are two good reasons to roll behind a screen. One is that players can gain meta knowledge from your rolls. If you roll an attack roll and announce the result, the player's now know the enemy's attack modifier. Which means they can figure out how likely they are to be hit and act accordingly. If you roll stealth, likewise, they now know how good the enemy is at stealthing or that they passed their will save DC 20 on a 19 so have a weak will save that can be targetted.
Secondly, it removes your ability to fudge the roll and while 99% of the time you won't be doing this, you've eliminated the 1% time where it's viable. You're not doing your PCs a favour. Most of the time when you fudge, you're doing it to assist them. You should also avoid giving them DCs. Get them to roll a stealth check, don't tell them the DC. Now they don't know if they've been seen or not and have to decide how hard they want to commit to their plan of action. It's tense. They don't need to know what the enemy guard rolled on his spot check or how good or bad his spot modifier is. I'm not saying everything needs to be super secret, panic if a roll goes wide, just that you'll find there's more drama and more excitement if the PCs don't see every roll and know every DC.

Have a plan for combat. You are going to need to track things. If you've ever watched Critical Role you'll see Matt's bizarre system for taking initiative from his players. Seems kinda weird but I guess with so many players it's a method he finds easier. To me it seems unnecessarily clunky. I use a sheet of paper and I write the inits for my players with gaps between. If my enemies are goblins with a +1 initiative then I expect most of them will roll around the 10-12 range so I'll leave bigger gaps there. I assign them letters. Goblin A, Goblin B, rather than numbers to avoid having Goblin 1 2 confuse me as to whether this goblin has 12 initiative or not.
I put their HP in a circle on a separate sheet, along with their name again and adjust this as they take damage. This is important in 3.5e, don't track just damage dealt. You may need to know their current HP in case they take subdual damage for example or if their con mod gets reduced. If you're using massive damage rules, don't erase their starting HP, you may need to know this number.
If they are likely to take or inflict effects then I have a system for that. If an enemy is sickened for 4 rounds I write sick 4 and I count down not up. If it says sick 2, I know there are two rounds remaining. If you count up and it says sick 3 you now have to remember how many rounds they were supposed to be sickened for. Was it four or five? Eliminate the confusion, count down. Same goes for an effect on the field, ice storm left difficult terrain? Count down the rounds.
If it's a scrum with a lot of combatants, track who has taken an aoo with a simple mark, maybe an X or a tick or wiggly line, whatever works for you. Come up with other marks for things you need to track. If a player is suffering an effect that gives them a save at the start or end of every turn, have notation in mind. SAS or SAE in a circle works for me, save at start, save at end. Are creatures grappling? I use a g in a circle to the left of each grappler and link them with a line like manacles. I put temp HP in a triangle.
You'll learn what works for you as you go but simply be prepared, have a plan. In 3.5 more than 5e you will find there's a lot to track. Start with common stuff that will come up a lot, for example in 5e, have a simple way to indicate an enemy suffering from disadvantage, or that players have advantage against. Have a system in place for player abilities/spells that are gonna come up every session. You'll eliminate a huge chunk of combat related work, leaving yourself with just the edge cases to handle.

Take notes. Especially if you improvise anything. Named a throwaway NPC? Don't just write down their name. Be clear, Dahlia, Pink haired Elven snake charmer the PCs met outside Lando's bookshop in Dishville.
Organize your notes. When you get into a lengthy campaign things get messy. Have a system. For my biggest campaign, I had a list of places that included people met there, grouped by affiliation, with some notes and places the PCs know of there. Like this:

Se'traal

The Thunder (Goliath wrestler/boxer)
Liberty Dalliance (Zaria Zircone)
Johnny Flametongue (Popular bard)
Mungo (Gnome wizard, owns emporium)
Olaf (Owner of popular smithy)
Wilson and Coleman (Masterwork bows and crossbows)
Ned Wilson, proprietor of above
Ted Wilson, his dead brother
Inquisitive Mind (Wizard college)
Bluerose Bank
Lord Stanley Bluerose (Bank owner)
Lady Savannah Bluerose (Stan's daughter)
Brandon Chellith - Captain of the Watch
Talion Silverleaf - High Priest of Corellon
Lord Vincent Vestin - Overweight Gourmand
Dennis Stanch - Proprietor of the Dome
Lionel Eskelion - Spymaster
13 Crow Lane - Ditch-house
27 Key Lane - Matreus house
Tez - Lookout at the speakeasy/tailor's
Caspian Valentine - Dmitri/Claude's manservant
Peregrine Tarabella - Halfling Tailor
Briella - Elven Jeweller with tattoo sleeve
Black Lily - Criminal dealing cyan
The Magic Dragon - Wizard pub
The Bear Maiden - Dodgy Inn
The Suspicious Cat - Tavern where Pethmir's friend Joe works

Inquisitive Mind
Sebastian Wentworth - Headmaster
Archwizard Aelon Starswirl - Human Wizard

Se'traal - Clutch Taskforce
Savannah Bluerose
Haldur Lightmace
Toben Grimoire (cleric of St Cuthbert)
Sister Sophia (cleric of Wee Jas)
Maximilian Virtue (paladin of Heironeous)
Lord Claude Vasiliev (vampire/ranger)

Chestnut Circle
Skala - Human female
Poppy - Halfling Female
Lam - Chilled out elven man
Metcalfe - nudey druid leader

Ashfield Asylum
Jargaz (Ignatius) Inzadrir - Rethmir's father (Tordrek, his grandfather)
(Argentine) Davna (Giselle) Galthran - Rethmir's mother

This allows me quick lookup. If I need their specifics I can dig out their character sheet but sometimes, a simple note is all I need to recall the information about that character. I also have notes on locations and their relation to each other and a list of lore related things unique to this campaign and so on.
Ultimately I know what I can and can't remember and you will too with practice. I don't need to note that Savannah Bluerose has blond hair with a blue stripe and is a paladin of Pelor because I know it. I still remember that even though that game was years ago. Looking back at those notes, I know exactly who Tez is and what the tailor/speakeasy I referenced is. I know that Caspian Valentine was an ugly hunchback despite his nice seeming name. I know Sebastian Wentworth had a love of biscuits and could never remember his secretary's name. The list was just a memory prompt for a campaign spanning three years that had hundreds of NPCs.

I did some prep for sundry elements too. Why wait til a player asks what day it is to decide what the days are called? I named my days and months in advance and had them ready to go. I created a list of drinks that can be ordered with their prices so that can be pulled from at the drop of a hat. I have a file containing a description of every potion craftable in 3.5e so I never need to struggle to come up with one. It also helps track unknown potions the player's haven't identified, if months down the line they finally ID that potion that on their sheet simply says
"A deep purple with black sediment, this potion smells like woodsmoke but surprisingly has no flavour."
I can instantly look it up and know it's a potion of Darkvision.
These are small touches but each one helps cement that reputation with your players that you know what you're doing.

What I'm getting at is, make notes on the spot if you have to make things up, but have an organised system to transfer those notes into. Have enough info that you can pull the place or character to mind. Keep detailed notes separate that you can reference if you need more specifics. Anything you give your players that isn't immediately identified, have a way of checking it six months from now when they remember they still have it. Maybe a sheet of things they haven't identified yet that you can cross off as they go, ie after they loot, note the description of anything they didn't identify and in brackets what it actually is. Then when they are like, hey we never figured out what this ring with the blue gemstone in the shape of a eagle does, you can check your notes and know exactly what they are talking about.

Finally, sometimes you're not gonna have an answer. There's gonna be rules you can't find (especially if you're playing 5e) or edge case scenarios that the rules don't explicitly cover. If you can't find it within a few minutes, make a ruling. Make it clear the ruling is temporary until it can be checked out of session. And then follow up. Check it out of session. Check the Rules Compendium, Sage Advice, Giant in the Playground or Stack Exchange or commit to how you want it to work and then tell your players at the start of next session. Ok, that rule we couldn't figure out last week, here's how it works going forward. And for god's sake, write it down somewhere.