If you have an idea for a character but don't know what to do with it, here are three easy steps that will help you create a great story:
1. find out what your main character wants most and make him/her want it or need it more and more.
2. find something that prevents him/her from getting that thing and make the obstacle bigger and more urgent (it can be internal, another character, or the world your character is in).
3. bring the conflict to a head until the character resolves it by getting what he/she wants, letting go of what he/she wants (and possibly getting something better in return), or coming to accept being without the thing he/she originally wanted.
A plot can have several steps, so your main character can start out wanting one thing, get it, and then want something else. For example, in The Cat in the Hat, the main characters ("me and Sally") want something to relieve their boredom until they get it; then they want to avoid getting in trouble.
These three steps have infinite possibilities depending on the main character(s), other characters, setting, style, and want/need.
If you have an idea for a plot but not a main character, you can easily turn that plot into a main character, too: whatever the objective of the main character in a plot is supposed to be, create a character who is strongly motivated to achieve that objective. Create other characters who are strongly motivated to stop the main character from achieving that objective. For example, some of the people who are motivated to solve a crime are a detective, a reporter, the accused, the victim, and the likely next target. Notice that the more motivated the character is to achieve the objective, the more compelling the story becomes.