I'd like to know in which cases may, might, must, can, should, shall are supposed to be used.
That's much too big a question to answer in one thread. Try posting individual sentences in which you are unsure which is the most suitable modal.
Context is important. Please provide enough for us to be able to deal effectively with your question.
Your thread title should include all or part of the word/phrase being discussed.
If you just want to know the meaning of a word, try OneLook Dictionary Search first.