"Yeah" sounds pretty rude if you don't know the person you are talking to (ie. you don't know if they would accept "yeah" as a response). If in doubt, use "yes".

When you want to answer in the affirmative.

Yeah is a laid back version of Yes. Most of the time you will want to use yes when answering questions in a professional environment. (School, Work, Meetings, etc.) Yeah is reserved for use around friends, family, and casual interactions.

Every time I use "yeah" around my mother, she says, "You're a teacher. You should say 'yes.'" Which means that if you're a professional or in a situation where more formal language is required, you should use "yes." That said, my conversational style is casual, so I usually use "yeah." "Yes" sounds very stilted for me, and I don't use it unless my answer needs to be very clear or if I want to emphasize my answer ("Yes, yes, YES, I said I would do it!"). "Yeah" for me also can mean "uh-huh" (meaning "I'm listening and following what you're saying").

Yes is used for formal occasions, yeah for informal occasions.