The past tense of should is should have + past participle. Had better is similar, but it's used for more urgent advice with bad consequences if you don't follow it (eg. You had better quit smoking or you'll die).

Had better VS should examples?

If you do come, I can give you a lot of suggestions and advice. For instance, everyone who visit's the Big Apple should go to Central Park. If you're a smoker, you had better not smoke there, because smoking is illegal in NYC parks. ... We use should this way when we want to give a suggestion.

Should had VS should have?

Had is the past tense of have and has, however, we don't use 'should has' even for 'she'. For example, she would have... (NOT she would has). Thus, always use 'should have'.