The auxiliary verb should, used as a conditional, expresses recommendations or suggestions:
You should talk to him. I recommend that you talk to him.
The employees shouldn't behave like this. It's my opinion that the employees behaving like this is not a good idea.
Should I bring something to eat? Would it be a good idea for me to bring something to eat?
Should sometimes expresses probability:
Horatio should be in his lab right now. It's probable, expected or likely that Horatio is in his lab right now.
The results of the vote should satisfy everyone. The results of the vote will probably satisfy everyone.
Should can express duty and obligation, but is less strong than have to and must:
You should be wearing your seat belt. You are obliged to wear your seat belt.
For a past action, we use should + 'have' + past participle:
Kalvin Krime should have hired Horatio while he was available.
Should like to allows us to express a wish in a polite way. In informal English, would is more commonly used.
I should like to visit Uganda one day. I would like to visit Uganda one day.
Note: The auxiliary verb ought to is a synonym of should:
I ought to go = I should go.