This one's for the first time Keepers, Dungeon Masters and other would-be screen monkeys out there. You know who you are.
The first time's always the worst, but it's often the most fun too. There you are, notes in hand, dice at the ready. Maybe you've got some theme music all queued up on your tablet, maybe you've spent all week getting the room just right, or maybe this is something you're doing on the fly, with little or no preparation. How you've come to this dark night of the soul doesn't matter; what matters is, you're here, and you're willing to go through with it. Well done! This is a feat right up there with public speaking and open mike night, and the audience is restless. So very restless ...
Let's get you started.
Rule Number One: Don't Panic. Remember, though it may feel like the world will collapse at any moment, there's nothing important at stake here. Nobody's going to die if you make a bad call at the gaming table. The roof won't cave in because Bungo Badaxe happened to fumble a combat roll and is now Dwarf tartare on the dungeon floor. So long as you remain calm and confident, even the worst gaming fumbles can be dealt with. Don't let yourself be bullied into any hasty decisions either. This is your game. Run it.
Rule Number Two: Know the Rules (But Not That Well). It goes without saying that you ought to have a decent grip on the system you happen to be using, whether it's as simple as Toon or as complex as First Edition Advanced Dungeons and Dragons. What you want to avoid is being that guy, the one who sits there poker-faced and spouts, 'Actually, I think you'll find that on page 298, paragraph 4, subsection c of the Goblin Fluffer rules, it says ...' NO. Just no. Only rules lawyers need that level of detail, and even they don't really need it; it just makes their dark, withered, twisted hearts feel a little flicker of joy. You need to be expert in the main mechanic, whatever that mechanic may be. In a combat-heavy game, like pretty much any iteration of Dungeons and Dragons, you need to know the combat rules backwards and forwards. In a magic-heavy system, like Ars Magica, you need to know the magic rules. Everything else can be a little fuzzy. See also Rule One.
Rule Number Three: Play Fair. There used to be a lot of discussion in the D&D world about whether the DM should make all his dice rolls behind the screen, or out in the open. Behind the screen preserved mystery, but it also allowed the DM to fudge, or even cheat. The players knew this, and often resented the screen. Me, I've always been a dice out in the open guy. Let the chips fall where they may, because when it comes right down to it, the players need to know the DM is playing fair. Everyone at that table wants to be the hero, and you're not helping if you start playing favorites. Sometimes this can mean stepping in when one player's hogging all the spotlight time - the game needs to be fair for everyone, not just your best buddy Bob - but more often it means you need to be completely open in all your dealings with the group.
Rule Number Four: Know What Your Players Want. Tabletop gaming is all about entertainment, and that means you need to cater to your audience. You may be in love with the intricate power struggle between noble houses that you've been carefully designing for years, hoping some similarly Machiavellian players will want to get involved in the high-level politics and scheming. None of that matters if all the players actually want to do is bash goblins for lulz and loot. They will be bored by your intricate plot, and you'll be tearing your hair out trying to get them to pay attention to the stuff nobody cares about but you. Find out in advance what kind of game your players want to get involved in, and design around that premise.
One of the big advantage Storyteller systems have is that player involvement in campaign world design is expected, which gives you a pretty clear idea of what everyone wants to see happen in-game. But there's no reason you shouldn't get the players involved in world design for every system, Storyteller or not. It doesn't have to be detailed; some players aren't comfortable getting involved in worldbuilding. If that's the case, just get them to describe one aspect of, say, the starting city. Is there a tavern they always go to? What's it called? Who works there? Even reluctant worldbuilders can answer questions as simple as that, and you can build from there.