There are two parts of character development: the part which builds characters to tell your story, and the part which defines who those characters are/what they are like. I always start with the first part, and get my characters from that. However, your question is dealing with the second part of character development, so I will address that.
Knowing the Character
The first step in developing any character is knowing who they are, and why they exist in your story. First, ask yourself how important the character is. Is he the main character? A secondary protagonist? A side character? A mere passing acquaintance? Knowing the answer to these questions will help you gauge how important your character is to your story. Only the important characters need serious development; those below them need only a basic direction, and those characters which we see only for a chapter or two need very little development indeed. That being said, it is best to err on the side of too much development, rather than too little. Know the importance of your characters, and how much development they need.
The next question you must ask yourself is, 'what is this character's role in the story?' Why are they in it? Could the story be told just as well without them? If so, that's a hint that they have no role whatsoever, and should likely be removed from the tale completely.
The main character is there to show the reader the story. The side characters are there to support the main character, do things he cannot, or sometimes provide contrast or support to the main messages of the tale, if you have them. Passing characters are there to move the plot along, doing necessary things.
Knowing the role of the character will give you a big hint as to what you need that character to do. You know the reader needs to like the main character, so he should therefore have a trait that the reader can get behind. You also know he's the kind of person who goes on an adventure to (insert goal here). What does that say about who he is?
You know side character A needs to provide hope to the main character at a critical time during your plot, so she should have a personality which will allow for that. She likely shouldn't be a pessimist, for example. She probably doesn't give up easily.
The character who sells your protagonist horses for the journey, however, likely doesn't need much in the way of development, as we'll only see him in a few scenes. Maybe he's a horse-lover. Maybe he likes peace and quiet, and is surly towards your companions. A handful of basic traits is all you really need to make passing characters seem life-like.
The above should help you to get a basic idea of what kind of people your characters are. That step is very important. It creates the base from which you can explore your characters further.
I like to write down all of the traits for my characters, sorted by person. I then look at one character's traits, and think about what that says about the person. If I know that character B likes hunting, is a renowned runner, and has explored the village river back home, I can conclude that this person might be adventurous. Maybe he likes the outdoors. From that, I can further speculate that he might not like being inside. Maybe he's claustrophobic. (Ah! A fear - well-developed characters aren't all smiles and sunshine.)
On the other hand, if I know that character C eventually betrays the hero, and does this for money, that says a lot about that person. Why would she betray her friend for money? Does money perhaps mean more to her than friendship? Was she perhaps betrayed herself by her 'friends' at an early age? Continue speculating, and you'll soon have a rich list of traits.
The Stat Sheet
You also of course need to know what your character looks like and how they act. What they look like is entirely up to you, but try to avoid going down the path of assigning 'quirks' to each of your characters simply to tell them apart. If you know your characters as 'the one with the scar,' 'the one with a limp,' and 'the one with white hair,' then you have a problem. Those aren't character traits. They are crutches. Only assign your characters such physical marks if they aid the story.
A better question to ask yourself is how your characters act. You now know their traits, so how do they interact with other people? If you're unsure, try this exercise: write a short piece about your character in a room with another basic character. This basic character has only the most rudimentary of traits - he's only there for your character to react to. Have the characters ask each other questions, pose riddles, try to escape the room, anything which seems natural. Doing this exercise can often reveal things about your characters you didn't know. You can keep the piece of writing when you are done or throw it out; it's served its purpose.
Once you know how your character view and interact with others, it's time to ask yourself how they view and interact with themselves. We all discuss things over with ourselves. We all have our own images of ourselves (which may or may not be entirely accurate).
What does you character think of himself? Is his opinion better or worse than he actually is? Why? Is he spot on? What made him come to such an accurate conclusion?
Something else to consider is fantasies. We all have dreams which we would tell no one else. Your characters should be no exception. You know their traits, you know who they are - what would their deepest desires be? What about their greatest fears? What are the secrets they would never divulge, and why?
Answering these questions will help you turn your basic characters into fleshed out creations which feel authentic to readers. The more time you invest in a character, the more real they will seem. There's no magic formula to make a character seem real. You just have to work at it, and put a lot of time into it.
One thing you should not do, however, is fall back on cliches. Cliches aren't all bad - after all, they are popular because they get the job done - but they have been used so much that they now feel stale and contrived. If, at any point, you find yourself thinking that you have seen the character you are creating somewhere else, in a book you read or a movie you saw, STOP IMMEDIATELY. An overused character cliche might have found its way into your writing (this also might not be the case; be sure). A problem I find that I have is that I will assume one trait means another, when in fact it is simply a well-established cliche which my mind automatically leapt to. Watch out for that.
Strive to be original. If you are creating an elf, don't assume that he has to be slightly taller than a human, fair-skinned, pointy-eared, strong, and capable of wielding magic. Make him face plant now and then. Have him miss the point of a joke. Have him develop a cold. And perhaps most importantly, make him be the worst shot with a bow in all the land. That will make for an original elf.
So, how can you make well-defined characters? Time and effort. Know what role your characters play in the story, and why they are there. Know how important they are, from protagonist to a stable boy mentioned for two sentences.
Define what they do, and what those actions say about who they are. Get a basic feel for what kind of person they are. From there, speculate. What does this base say about them? What can you assume about this character? What can you assume this character is not like?
Determine their appearance, actions, interactions, and internal thoughts. Thoroughly explore them. They might not know exactly who they are, but you do. If you know them, it will come across in your writing. When you write, you won't be writing characters in a book.
You'll be writing real people.
Best of luck!