This document summarizes the use of several modal verbs in English:
1) Can, must, should, and ought to are used to talk about permission and obligation. Had better expresses stronger advice or warnings about the immediate future.
2) Have to and have got to also express obligation, with have to used in any tense and have got to used for specific occasions.
3) Need, don't need, and needn't are used to talk about necessity, with different forms used for habitual versus specific instances.
4) Be able to, be allowed to, be permitted to, and be supposed to can be used instead of can, particularly in formal contexts, to talk about what is