The purposes and basic traits of a character is a must-have when you are going to develop them, it is like a rough sketch to paint a full-color image from. Have that backbone first, usually you already have it when generating idea for your story.
After that, you match the backbone with the situations in the plot you will throw them into. Last step is to either rationalize or reference (or both) how would they react and behave in such situation, you can reference it by consuming media containing similarly-natured character, or if it possible ask people you know and trust with same disposition.
I also go back-and-forth when developing, for cross-checking if they behave consistently and true to their designed purpose or nature. I took mental note and also train myself "acting" as them by imagining them in various scenes and various situations.
For me, personality quizzes has helped me a lot in term of fleshing out and developing my characters. By taking the quiz, I train myself to think in my characters' shoes and sometimes faced with questions that said characters will never encounter in the story.
One note: your character will inevitably change as the story progress, or as you develop them, or as your skill develops. It is very natural that as we grow up and widen our perspective, they do grow up too. If the author has character development, the characters too.