You use can when you are mentioning a quality or fact about something which people may make use of if they want to.

You use can to indicate that someone has the ability or opportunity to do something.

You use cannot to indicate that someone is not able to do something because circumstances make it impossible for them to do it.

You use can to indicate that something is true sometimes or is true in some circumstances.

You use cannot and can't to state that you are certain that something is not the case or will not happen.

You use can to indicate that someone is allowed to do something. You use cannot or can't to indicate that someone is not allowed to do something.

You use cannot or can't when you think it is very important that something should not happen or that someone should not do something.

You use can, usually in questions, in order to make suggestions or to offer to do something.

You use can in questions in order to make polite requests. You use can't in questions in order to request strongly that someone does something.

You use can as a polite way of interrupting someone or of introducing what you are going to say next.

You use can with verbs such as 'imagine', 'think', and 'believe' in order to emphasize how you feel about a particular situation.

You use can in questions with 'how' to indicate that you feel strongly about something.