Il verbo Shall traducible con 'dovere' non è molto usato ad eccezione delle forme interrogative con I e We:

esempi:
Shall I go? (devo andare via?)
Shall we go? (ce ne andiamo?)
Shall I help you?
What shall I study?

il verbo modale Should

Should (traducibile spesso con dovrei, dovresti, dovrebbe, etc...) invece si usa per:

• dare consigli e suggerimenti:
  esempi:
  You should study for my test
  You should go to the doctor
  When you go to Rome, you should go to that restaurant
  She shouldn't skoke so much.
  
• esprimere obblighi:
  esempio: You should be at work at 9:00
  
• esprimere aspettative:
  esempi:
  Sarah should be arrived by now
  Sarah shouldn't be arrived yet

aforismi con should:

All married couples should learn the art of battle as they should learn the art of making love.
Ann Landers

A man should look for what is, and not for what he thinks should be.
Albert Einstein

Everyone should be respected as an individual, but no one idolized.
Albert Einstein

A baby is God's opinion that life should go on.
Carl Sandburg