You use should when you are saying what would be the right thing to do or the right state for something to be in.

You use should to give someone an order to do something, or to report an official order.

If you say that something should have happened, you mean that it did not happen, but that you wish it had. If you say that something should not have happened, you mean that it did happen, but that you wish it had not.

You use should when you are saying that something is probably the case or will probably happen in the way you are describing. If you say that something should have happened by a particular time, you mean that it will probably have happened by that time.

You use should in questions when you are asking someone for advice, permission, or information.

You say 'I should', usually with the expression 'if I were you', when you are giving someone advice by telling them what you would do if you were in their position.

You use should in conditional clauses when you are talking about things that might happen.

You use should in 'that' clauses after certain verbs, nouns, and adjectives when you are talking about a future event or situation.

You use should in expressions such as I should think and I should imagine to indicate that you think something is true but you are not sure.

You use should in expressions such as I should like and I should be happy to show politeness when you are saying what you want to do, or when you are requesting, offering, or accepting something.

You use should in expressions such as You should have seen us and You should have heard him to emphasize how funny, shocking, or impressive something that you experienced was.

You use should in question structures which begin with words like 'who' and 'what' and are followed by 'but' to emphasize how surprising or shocking a particular event was.