1. Start with a concept. This is how most of my characters start, and they usually begin with two or three word descriptors. "Demon stallion" or "spoiled dragon prince" or "psychic dolphin". Characters as this stage are more anima than anything; they are forces at play in the primordial soup of story. When an idea is this new, I try not to focus on it too much. Ideas need time to germinate, and I've found myself disappointed in times past when the potential of the character was so much more exciting than the concrete reality of what they became. Since during this time I'm developing plot and main conflict, I try to move characters around and see who I gravitate towards. This helps story and character grow organically. It's during this time that I try and determine what the character struggles with, the yin and yang of their internal difficulty. For example, I was recently asked to come up with a character for an urban fantasy roleplay, with no real details about the world other than it would be similar to Buffy: contemporary setting, high-schoolers fight evil, etc. My only other bit of information was that each character could have a magical or supernatural element if they wanted. I immediately came up with the idea of an extremely stoic, gentle, laid-back hippie type that had strong values in helping people and being a pacifist. But he would have some kind of curse on him, something that would wipe away his conscious mind and turn him into something monstrous and out-of-control. Regardless of the trappings of this character (i.e., whether be became a vampire or a werewolf or possessed by a demon), at his core he had a fantastic conflict going. His concept was peaceful-guy-cursed-to-violence, and I was quite excited to see how he would cope, what his journey would be. (Too bad that roleplay never materialized, but whatever.)
2. Determine role and archetype. This is an important next step to figure out your ensemble. I've heard it said that sometimes writers can try to cram too many characters into a story when really they have a character who belongs somewhere else. Studying story structure like Hero's Journey and 20 Master Plots and TvTropes comes in handy here. If you've got two Lancers, or two The Hearts, or everyone is a The Stoic, maybe your characters need some mixing up. Character concepts are a lot easier to abandon or change at this stage. Also, creating characters for a novel is not as willy-nilly and full of wild abandon as creating one for RP (or it shouldn't be). Characters should have a point, and major ones have important roles to play in plot and in developing believably. Believe me when I say that telling yourself "Eh, this'll work itself out later" will run you facefirst into difficulty. This is more of a "homework" stage than any other, because it requires knowledge of literature and story structure. (At least for me.) Knowing plot elements can sometimes develop your characters, too: "A baby-killer might be interesting
ooh! What if one of the characters failed to save a baby in the past?" And so on.
3. World-build for the character.At this point, I've unusually figured out major tectonic plates in story and world. Countries, races, politics, race relations, relationships between countries, cultures, beliefs, and so on all influence my characters. Of course plot and world can affect character and vice versa, so don't think any of this is some kind of one-way thing. For example, my "spoiled dragon prince" concept. I started asking questions. "Why is he spoiled? Why's he a dragon? What kind of royalty rules?" I eventually figured out that my prince was as spoiled because his people's ability to transform into dragons made them demi-gods, and that they were worshiped by a strict caste system. The power of the regency and their caste system created ripple effects in the world-building: their country was highly xenophobic, with heavily controlled borders, and countries on the outside saw the dragon people as crazy powerful and not someone you'd want to mess with. Then I thought "What if someone did want to mess with them? What if they decided 'You know what my army could use? Dragon soldiers.'" My first major piece of plot arose out of world-building for the character.
4. Create an arc for the character. By this point, I'm filling out a character sheet. Likes, dislikes, flaws, fears, things that will help me figure out the why of what the character values and sees as important. These ideally provide story stakes. This is also when I have to figure out the change that will occur in the characters and (hopefully, but not always, damn you, Tokotsi) how it comes about. Plot by this point is usually fairly figured out; I keep an outline in a text document that can be changed if the need arises. But I keep my outline vague enough to keep room for organic changes; you never know when things will develop and surprise you during your actual writing. My characters need to be pretty concrete, but not necessarily the story. I usually don't name my characters until this point, because I like to keep them as forces for as long as possible. Naming a character brings them to life, and it's kind of a point of no return for me. Almost all of my characters have secret meanings in their names, and I'll spend hours looking up things just so I can feel clever. But that's a writing quirk of mine, not a hard and fast rule. None of these are.
5. Play with the characters. One of my favorite moments in starting a novel is the chance to get to write a character defining moment. The first time the character shows up, they behave immediately in a way that establishes them. A lot of writers seem to struggle with this, and I suspect its because they forget to play with their characters. Roleplay taught me how valuable it is to just put a situation in front of a character and see how they'll react. I tend to talk to myself in the car or when I'm cleaning, acting out characters. And just letting them interact with each other, or with problems. I've gotten quite a few good scenes and pieces of dialogue by doing this. Other writers say they interview their characters or act as a therapist for them. Whatever you're doing, do it a lot. You have to know your characters inside and out, so that their behavior is believable and heartfelt. Strong characterization is one of the most important things in writing, and you need to practice the skill of characterizing as much as possible.