Should is a modal verb. It is used with the base form of a verb.
1 modal You use should when you are saying what would be the right thing to do or the right state for something to be in.
I should exercise more..., The diet should be maintained unchanged for about a year..., He's never going to be able to forget it. And I don't think he should..., Sometimes I am not as brave as I should be..., Should our children be taught to swim at school?
2 modal You use should to give someone an order to do something, or to report an official order.
All visitors should register with the British Embassy..., The European Commission ruled that British Aerospace should pay back tens of millions of pounds.
3 modal 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.
I should have gone this morning but I was feeling a bit ill..., You should have written to the area manager again..., I shouldn't have said what I did.
4 modal 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 should have no problem with reading this language..., The doctor said it will take six weeks and I should be fine by then...
5 modal You use should in questions when you are asking someone for advice, permission, or information.
Should I or shouldn't I go to university?..., Please could you advise me what I should do?..., Should I go back to the motel and wait for you to telephone?...
6 modal 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.
FORMAL I should look out if I were you!
7 modal You use should in conditional clauses when you are talking about things that might happen.
FORMAL If you should be fired, your health and pension benefits will not be automatically cut off..., Should you buy a home from Lovell, the company promises to buy it back at the same price after three years...
8 modal You use should in `that' clauses after certain verbs, nouns, and adjectives when you are talking about a future event or situation.
He raised his glass and indicated that I should do the same..., My father was very keen that I should fulfill my potential...
9 modal 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., (vagueness)
I should think it's going to rain soon...
10 modal 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., (politeness)
I should be happy if you would bring them this evening...
11 modal 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. SPOKEN, emphasis You should have heard him last night!
Should've is the usual spoken form of `should have', especially when `have' is an auxiliary verb.