[subject] + 应该 + [verb]
[subject] + 不应该 + [verb]
该 + [verb] + 了
应该 goes before the verb and says what is right or advisable – "should", "ought to".
The negative is 不应该, "shouldn't".
Chinese has no separate form for "should have". A time word or the context puts 应该 in the past.
应该 also says something is very likely: "should be", "must be by now".
The place of 不 tells the two senses apart. 不应该 is "shouldn't"; 应该不 is "probably not".
In speech 应该 shortens to 该, and 该 + verb + 了 says it's time for something.
应该 is advice. 得 and 必须 say you have no choice; each has its own point.