Brainstorming is a proven technique for exploring just about any idea. The process consists of quickly recording (without editing yourself) all of the options/descriptions/ideas /thoughts you have about a topic. You then sort through your items and pick the ones that work. This process can easily be applied to creating characters.
I have purposely tried to leave the sort of details you should review as vague as possible. If you really need more guidance, however, you might want to start with appearance, friends, goals, quirks, flaws, problems, values, morals, history, possessions, skills, fears, favorites, enemies, education, finances, pets, and family. Don't feel as if you need to include all of these categories or limit yourself to these categories. Just write what comes to mind.
Step One: Find a way to organize your thoughts
Get a large sheet of paper, notebook, a set of index cards or a computer application that you can use to write ideas on.
Step Two: Write what you know already
Write down the information that you already know about the character. This could be as basic as the name and gender. The point is, get the things that you are sure about out of the way first.
Step Three: Explore the possibilities
Begin writing down every possible potential detail that you can think of for the character. The details can be random and even contradictory. Your record every possible thing you can think of that seems to fit the character. Spend as much time as you need, but no less than fifteen minutes.
Step Four: Figure out what matters
Review the potential details and discard details that you are sure won't apply to your character. Separate the rest into details you are absolutely sure that you want, details that might work, and details that are still interesting but contradict each other.
Step Five: Build your profile
Create your profile of the character, grouping details into categories of similar items. Concentrate on the details you are sure about but give the other details a final review to decide which ones should be added.