[subject] + should have + [past participle]
[subject] + shouldn't have + [past participle]
Should have looks back at the past and says what would have been better. With I or we, it is usually a regret: you are sorry about it. With other people, it is often a criticism.
The verb after have is the past participle (gone, done, told), never the base verb or the past simple.
Shouldn't have says that something happened and it was a mistake.
In speech, should have sounds like should've. You can write should've in messages, but never should of.
Put should before the subject.
Should + base verb gives advice about now or the future. Should have + past participle is about the past, when it is too late to change.