Not sure what kind of material you're playing from, but if it's something with visuals (or lots of description), my advice would be to take a look at their surroundings to get a good feel of their environment. What sorts of things are laying around (what things aren't), what kind of city/town/random spaceship/etc did they grow up in, who all might they come in contact with on a daily basis, how is their room or house decorated? Etc.
I play a minor character from a video game and what I did was tried to incorporate those sorts of things in my headcanon to make it more believable. (Like, for example, mine lives in a city with lots of machinery going all the time, so he finds it hard to concentrate when there isn't some kind of background noise.) Even stuff like how a character dresses or talks can tell you a bit about their personality or how they were raised. Another thing you might want to look into is what other characters say about your character (if they do). Sometimes they can throw out hints, too.
Compared to a main character, it's kind of like working backwards sometimes, but that can also make it a lot of fun. Hope that helped at least a little!
Re: GENERAL: MINOR CHARACTERS
I play a minor character from a video game and what I did was tried to incorporate those sorts of things in my headcanon to make it more believable. (Like, for example, mine lives in a city with lots of machinery going all the time, so he finds it hard to concentrate when there isn't some kind of background noise.) Even stuff like how a character dresses or talks can tell you a bit about their personality or how they were raised. Another thing you might want to look into is what other characters say about your character (if they do). Sometimes they can throw out hints, too.
Compared to a main character, it's kind of like working backwards sometimes, but that can also make it a lot of fun. Hope that helped at least a little!