There are a lot of resources about how to design a character available on the Internet. Conventional wisdom is that you should have an extremely clear idea of who your character is before you sit down to put the story to paper: figure out what they look like, how they talk, what they want, etc.
If you're interested in that, I'd recommend googling "20 questions." It's good advice, in general. A story thrives on details: the more you know about what's going on, the better a picture you can paint and the more smoothly getting it out is liable to be. Details are fundamental to consistency, and consistency is fundamental to the suspension of disbelief. If you're generating a major character, I'd recommend doing it the old fashioned way.
However, I'm not going to talk about that today because, frankly, everyone talks about that. You don't need me for it.
I'm going to talk about a less discussed alternative technique which I learned from running roleplaying games. These were situations where I didn't have the luxury of time. When you're running a game, you often need a minor character right now, it's important to be able to do that. It's also good for bit parts in novels, and I have, in fact, even used it for major characters in my stories. I call it 'organic character development.'
The way this works is simple: form a dim picture of a character in your head. Enough that you could say something about them. Are they male or female? Can you tell me one sentence about them?
For example, I'm thinking about a private eye. His name is Jones. He's got... oh, brown hair. Thin, but not gaunt.
I don't know anything else about this guy yet. I don't let it worry me, though. Instead, I just run with what I do know.
As soon as I need another detail because it would be relevant in the story, I do two things:
1) Make up something that sounds good.
For instance, a leggy dame comes into Jones' office with a problem - a classic story hook for old timey detective stories. I need to know how he reacts. Is he a lech, or professional? Is he maybe gay? Does he banter, or is he businesslike?
Whatever you pick, it should be interesting enough to be worth mentioning at all, and it should serve the story at large. Never pick something that you think is boring.
In this case, I think Jones is all a bit of a wise guy who likes to flirt. I mean, that's a classic, and why would I be writing a detective story if I didn't enjoy the classics?
2) Write down what you've made up, keep it straight.
This would be the real trick to organic character development: things are fluid until you make a decision, but once you have decided, you need to stick to it. For the rest of his appearances, Jones needs to be a flirty snarker.
Moreover, later decisions that I make about Jones should support this conclusion generally: it's now too late to give him a hook for a hand or other serious physical impairment that would impact his romantic prospects, because if he had one, it should have come up in his initial scene flirting with someone.
The more decisions like this you make, the more a character goes from blurry to very focused and specific. If Jones keeps popping up, my audience will get to know him at the very same pace that I, the author do. Which is actually pretty cool when you're doing it.
And... that's actually all there is to it. Step (2) is where most people run into trouble, which is why I recommend making notes as you go. Start a traditional character profile - 20 questions style - and fill it in as you work.
Several major characters in my first series actually came about like this. If I ever get around to sharing it online, I'll talk about which ones and what that was like, but no promises - still a little disorganized on the point of, "What do I do with rough drafts of four books in the drawer, and another in process?"
Anyway, I better get to school. Time to learn about taxation and government organizational structures in detail, and I'm excited. Yes, really. Maybe I'll talk about economics sometime, too. :)