We can often use should or ought to with little difference in meaning when we talk about
OBLIGATION a n d PROBABILITY.
Obligation
---- giving ADVICE or making a RECOMMENDATION:
• 'This fish is too cold!' 'You should / ought to take it back.'
• You'll catch cold if you go out like that. I think you should / ought to take a hat.
or saying what an outside authority recommends (although we prefer should in this case):
• The manual says that the computer should be disconnected  from the mains
before the cover is removed, (not ought to be....)
However, we use should (or would), not ought to, when we give advice with I:
• I should leave early evening, if I were you. (or I would leave...; or I'd leave...)
-----Talking about a RESPONSIBILITY or DUTY:
• People should / ought to be warned  of the danger of swimming off this beach.
• I should / ought to visit my parents more often.
Probability
----saying that something is PROBABLY TRUE now or will probably be true in the future:
• 'Have we got any string?' 'There should / ought to be some in the kitchen drawer.'
• You should / ought to have received the report by now.
• I enjoyed her first novel, so the new one should / ought to be good.
We use should / ought to + have + past participle to talk about an obligation in the past. We often
indicate some criticism or regret:
• He should / ought to have asked me before he took my bike.
• We should / ought to have taken a taxi when it rained.
----We also use should / ought to + have + past participle to talk about an expectation that something
happened, has happened, or will happen:
• If the flight was on time, he should / ought to have arrived in Jakarta early this morning.
• The builders should / ought to have finished by the end of the week.
We can use had better instead of should / ought to, especially in spoken English, to say that we
think it would be sensible or advisable to do something. However, we don't use it to talk about
the past or to make general comments:
• If you're not well, you should / ought to ask Ann to go instead, (or ...you'd better ask...)
• You should / ought to have caught a later train, (not You had better have...)
• I don't think parents should / ought to give their children sweets, (not ...had better...)
When we make a logical conclusion from some situation or activity, we use must not should or
ought to.
----- You must be really mad if you think I'm going to lend you any more money.
 It's the third time she's been skating this week - she must really enjoy it.
We can use supposed to instead of should / ought to to talk about an obligation to do
something. It is commonly used in spoken English to express a' less strong obligation:
• I'm supposed to be there at 10.00. • The work was supposed to start last week.
We use (be) supposed to when we report what many people think is true:
• Eating sweets is supposed to be bad for your teeth..

Here is some examples:

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

Should can also be used for obligation. For example:
- I should call my Dad next week.
- He should apologize to Kerry.

Should is also used for when something is expected.
- Tony should arrive here at 13.00.
- It's 13.30, and Tony should be here.
- This book is wrong, tha answer should be "B".

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.)