First thing to keep in mind about running a game, above anything else, is that you're there to have fun. As a DM, you're responsible for making sure your players are having fun, but they're equally there to help make sure you and the other players are there to have fun too; roleplaying is a cooperative hobby, and despite the most Gygaxian opinions in the community, it is not 'the DM versus the players', but the players and the DM working in tandem.
That said, you'll need to make sure to challenge your players. A game in which they sweep in, solve all the problems ever, and continue on their merry way is boring, for them and for you. A victory at the end of a campaign should be won with blood, sweat, and tears; a victory should come at nothing less. Feel at your fullest to test, strain, and make your players work for their victories, but don't hand them to your players. 
There are two aspects to keep in mind for a roleplaying game; colloquially, they're 'fluff' and 'crunch'. Fluff is description; your Non-Player Characters (NPCs), the area around you, why monsters are attacking the town, ect. Fluff is your friend, because fluff is the reason people care. Sure, you could write fifteen random monster encounters and call it a night, and in some games, that's perfectly acceptable, but there's no investment, and furthermore, the game won't be remembered. 
Crunch is mechanics; the class levels and abilities of your NPCs and encounters. These will be providing the majority of the difficulty; a party fighting against a warband of drow mounted on spiders, the tomb of an ancient sorcerer king, or the ramshackle abodes of a kobold mining camp is crunch mixed with fluff, with the actual difficulties provided by the raw mechanics, or the crunch. 
Fluff is not within the scope of this document to develop; each campaign has its own, and each DM, in particular, has their own style to spin on it. Crunch, however, is something we can work with.
 Now, a couple of things to keep in mind (which will be repeated at the end of this document so you can print it off and take it with you to game). First, dice averages. A singular dice will generally have an average roll of half the die's value +.5. So the average on a d6 is 3.5, a d20 offers a 10.5, so on and so forth. Because of that, you can help tweak combat encounters to ensure your party is adequately challenged.
Split encounters into three types; the 'easy', 'medium', and 'tough' challenges, or, for a slightly more fluffy, your 'horde', 'minion', and 'boss' challenges. A 'horde' challenge should have an AC (armor class) equal to the average 'to-hit' of your party (probably +3-+4) +5, so an AC of 10-11 should be adequate. With hordes, you should be throwing roughly twice to three times the party's weight at them. Seven goblins armed with butcher knives against a group is a challenge, trust me. Minions should be the average +10, so ACs in the 14-16 range, and equal to the PCs body weight. Four orcs with falchions is a solid challenge, especially for level 1s. Bosses should be the average +15; AC should be in the 19-22 range, and it should be one boss flanked with a minion or two. A wizard with skeleton minions is a good example.
For damage, do the reverse; figure out the PCs average AC. Your 'to hit' chances are based off of a d20, so a horde critter hitting a PC should happen 25% of the time (thus their 'to-hit' should be