Modal Verbs - English Grammar

shall:

In modern English Grammar, "shall" is only used in questions: Shall we drive?

should:

"Should" is used to ask for or to give advice ("should" or "ought to"): You should/ought to ask somebody for help.

"to be supposed to + base form":

• • You're supposed to call Nina as soon as you get here.
  • We were not supposed to be out at this time.

• "had better + infinitive without to":
  • Tom, you'd better do what I say or there will have to leave.