Had here is an unreal past; the meaning is present or future:
The contracted form of I had better is I'd better.
The negative is formed with not after better:
Had here is usually contracted after pronouns and in speech is sometimes so unstressed as to be almost inaudible.
Had better is not normally used in the ordinary interrogative, but is sometimes used in the negative interrogative as an advice form:
You had better is a very useful advice form:
In indirect speech, had better with the first or third person remains unchanged;
With the second person had better can remain unchanged or be reported by advise + object + infinitive: