Suggestions and obligations
Suggestions
We use should and shouldn't to make suggestions and give advice:
You should send an email.
You shouldn’t go by train.
We also use could to make positive suggestions:
We could meet at the weekend.
You could eat out tonight.
Obligations
We use must or need to to say that it is necessary to do something:
You must stop at a red light.
Everyone needs to bring something to eat.
You can wear what you like, but you must look neat and tidy.
We use mustn't for prohibitions – to say that it is necessary to not do something:
You mustn't make any noise in the library.
You mustn't say anything to her. It's a surprise.
We use had to (positive) and couldn't (negative) if we are talking about the past:
Everyone had to bring something to eat.
You couldn't make any noise in the library.