The base forms of verbs are used after the phrase had better, which acts exactly like the modal verb should, to suggest a required or desirable action.
Examples:
“You [had better][should] clean this room up before your father gets home.”
“I think we [had better][should] go home soon.”
“You [had better][should] hurry. The train leaves at three.”
“You [had better][should] not delay. Do it right now.”
“Since it is snowing heavily, I think you [had better][should] stay home.”
‘You (‘d) better leave …’ is spoken/colloquial but ‘had better leave’ is more correct. (Meaning, you should or it’s a good idea …)