Should is a modal verb used to give advice and recommendation.
- You should see a doctor.
- You should keep your promises.
- Should we buy her a present?

Should can also be used for obligation. For example:
- I should call my Mum tomorrow.
- He should apologize to Mary.

Should is also used for when something is expected.
- Tony should arrive here at 12.00.
- It's 12.30, and Tony should be here.
- This book is wrong, tha answer should be "A".

Note that have to inflects like a normal verb, it can have different tenses and uses auxiliary verbs for questions and negatives. For example:
- Do we have to go out tonight?
- You don't have to come with us.

Must doesn't use auxiliary verbs or different tenses.
- Must we go out tonight? (This sounds rather British, I really don't want to go out tonight.)
- We mustn't forget the tickets. (No auxiliary verb "to do", just add not.)

Ought to can be used instead of should. It is less common than should and sounds rather British.
- You ought to say thankyou for the present. (You should say thankyou for the present)

Negatives and questions are less common and even more British.
- We ought not to be late for the meeting.
Questions are often made with "Do you think.."
- Do you think I ought to get up earlier?

Questions with just ought to are rare.
- Ought I to get up earlier?

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