You don't want to think of non diatonic notes as having a relationship to the root (although it doesn't hurt to advance your knowledge of this) but instead think of them as "approach tones" or "passing tones". Unlike diatonic tones, approach tones are not typically notes you would choose to base a melody off of, but instead are used to "decorate" a melody: to give it more color, make it more unpredictable or exotic.

It takes a lot of practice to be able to use these notes effectively. Some common tips would be not to start or end your phrases with non diatonic tones, and try not to emphasize them on stressed beats. Try using them to connect chord tones (ex; c maj connecting 3rd to 5th..E F F# G) or to surround chord tones (5th to 3rd...G F# F D# E). Oh, and listen to a lot of jazz, especially be bop, so that you can get these type of phrases in your head.