"Had better" is poly modal. It is most commonly used to make recommendations. It can also be used to express a condition (if something doesn’t happen there will be a consequence). Structurally it functions as all modals do.
Subject + had better / ‘d better + verb.
Subject + had better / ‘d better not + verb.
* In informal English (spoken) you can use better to replace had better.
It is also possible to contract with proper nouns (spoken only)
Jane’d better get going.
You had better take your umbrella with you today.
That bus had better not get here soon!
He better get help.
You’d better take your umbrella with you today.
That bus’d better not get here soon!
He better not get help.