A character template is a handy thing - you start with gender, age, family background, physical description and, of course, the thing your character most wants or needs (the thing that drives them throughout the story). Really, that thing is what they believe will make them happy, just like us real people. A guy might believe a Maserati will make him happy, a girl might believe having Mr X fall in love with her will make her happy. But the question goes deeper than that. What both of them really want is to be loved and made to feel special. The guy believes the Maserati will attract the kind of gorgeous girl who will love him for himself, not the car - the car is "bait" and will make him look cool. Sadly, this kind of guy usually still loses out, or finds a girl who rips him off.
The girl who wants Mr X, on the other hand, may well find he is a horrible person and falls in love with his friend, Mr Y, who loves her and is perfect for her. Both of these situations could make a story. So you can ask yourself - what does my character believe (at the beginning of the story) will make them totally happy, and what actually does make them happy by the end? Just that shift alone develops your story in more depth, and in more interesting ways.
Another question to ask is what your character is most afraid of. Not spiders or heights, but deep down. Are they afraid of being abandoned? Of being poor? Of being unloveable? Some people have a fear of intimacy because of things that have happened to them - major betrayals, significant deaths. If you can place that character deep into the one situation they are most afraid of, you have instant conflict and a meaty story problem that is both external and internal.
You could ask what your character's secret dream is. Is it to win Wimbledon, when he is a good tennis player but not a world-beater? Why do people have unrealistic dreams? How close will he get to achieving it? What will he discover along the way? That he is a failure? Or that he is really the world's best coach and he finds a kid that will win Wimbledon and who he can help? And again, what does that dream really mean? Does he want fame and fortune, and sees tennis as a way to get it? He can still have it by being a winning coach, perhaps. Or maybe he ends up envious and vengeful.
I also like to ask what happened to my character in their life that makes them who they are. With someone who is only, say, 12, probably the thing that will affect them forever is going to happen right in my story, so I have to work with knowing enough about them to make the story real and meaningful. I also need to think about how they will deal with the terrible things that are about to happen to them, and how they will change and grow.
In writing about someone who is 40, I look at their childhood and their teen years. There is great potential to give a character backstory that deeply affects the story you are telling in the here and now. Did she witness a murder? Did he lose his father? Not every character has to be abused, by the way. It might be a good idea to avoid that, as it raises a whole other bunch of issues that may have nothing to do with the story you want to tell. Be judicious about this - you are the architect of this life. I like to ask students to write about their character in this way - what was something that happened to them as a child or teen that somehow changed the way they saw the world forever? What is their world view now? Optimist or pessimist? Do they believe in God or not? Are they cynical or fatalist? Are they trusting or wary? WHY?
I do a lot more than this - small things and large. It depends on the character. Some of them, like Tracey Binns, spring into life as if they were just waiting for me to come along and find them. Other characters I struggle with and have to write a lot of the story before I "find my feet" with them, and then the revisions change a fair bit. There are lots of small writing exercises that can help. A fun one I set in class is this: your character rushes out their front door (you decide where they're going and why they're in a hurry) and finds something dead (you decide what) on their doorstep. Write a scene that shows how they react, how they feel, and what they do about it.