That requires some creativity, some good ideas. If you don't have any, do what writers of roleplaying supplements have always done: steal. Take the world from your favourite series of trashy fantasy, and you have a usable RPG world right there! It doesn't have to be fantasy, of course, but most people are moderately familiar with such worlds from fairy tales, Tolkien and such, and that makes it easier both on your players and you. The world you'll play in is not totally alien, and neither is it our normal world (and thus less restricted in what is possible). Making up a world out of whole cloth and getting it believable is very difficult. Try it sometime and see.
For the purposes of this example, let's say that you do decide to use a standard fantasy world.
The next step is to decide what position you want your players to occupy in this world. That's a vital decision, so think about it for a while. While your players will design their own characters, you have to give them guidelines to work within. Those guidelines will to a large extent shape your campaign, so consider them carefully.
If you have any idea at all about what you want your campaign to be about, it should be rather obvious what limits you have to set on character creation. Some limits are very obvious. You don't want any astronauts in your fantasy campaign, for example (unless, of course, the point of the campaign is to dump some astronauts in a fantasy world and see how they cope). If you plan to focus on court intrigue, a peasant farmer won't fit very well. If you want a gang of adventurers who run around killing big monsters, someone totally without combat skills will be left out a lot.
Other limitations may be there just to make your job easier. Sometimes keeping the characters together can be difficult. If you've decided that they're all cousins and that if they don't take care of each other real good, grandma will come after them (and she's Real Bad News, grandma), they'll stay together a lot more than they would've otherwise.
Back to the example. We had decided on a standard fantasy world. Normally, I'd probably get thet idea for the world and what I wanted to happen in it at the same time. In this case, we just decided upon a world, and now we have to put some action in it. "Lowly people trying to make good" is a very classic theme in roleplaying (it was the standard theme for the very first published roleplaying game), and it can be lots of fun. So let's chose that one for our example.
Now, what demands does this make on our choice of characters? Well, roughly this:
We need to decide upon a few more things before we can start playing. Where is the campaign going to start, and roughly what do we want to happen at the beginning?
The classic place to start is in a tavern (actually, it's so often used that it has become a cliché). Since we have used old, tried and true ideas all the way before, lets do that now as well. The player characters will start in a tavern, and we will ask all players to tell us how their character came to be there at this time. We may not use the answers, but they may be interesting, and they will help the players get a feeling for their characters. If we are lucky, they will also give us ideas about what's going to happen.
So what is going to happen in the beginning, then? Somehow, we must get the PCs (that's "Player Characters", which you naturally guesssed at once) into some kind of action (and please note that "action" does not necessarily mean "violence"). If we're going to continue in the classic vein, and old, mysterious man will hire the party to do something. Since all charcters are out to make something of themselves (that's one of the design parameters we gave the players, remember?), they should be happy to get a well-paid job, even if it is slightly dangerous (it's probably horribly dangerous, but the old man isn't going to tell the PCs that, now is he?). Let's say that he'll hire the PCs to get rid of an evil wizard who has been terrorizing the neighbourhood for a while. That sounds as a decent, if slightly dangerous job. In reality, the old man just wants to get rid of a business rival and are hiring the PCs as a hit team. That way, we ensure that they will get into trouble later no matter what (either they have a nasty wizard for an enemy, or they'll have the local police after them for the murder of said wizard). Trouble is always good, it breeds drama and action.
Now we're ready to start. We now what kind of characters we're going to demand from the players, we know what kind of world we have, what kind of story we want, where they'll start and what will happen in the beginning. Time to call in the players.
Part 2: Starting the campaign.