‘Had’ is the past tense of ‘have’  ; but in the usage ‘ HAD BETTER’ , it has a present idea or meaning.  ‘Had better’ indicates an action which is preferable and in case of failure of action, it may bring about unpleasant consequences.  In other words  it suggests a course of action that seems advisable.

• He’s in a critical condition.  You had better visit him today itself.( i.e otherwise,sometimes, you may not be able to see him.)
• He’s a dishonest man.  You had better keep an arm’s distance with him.
• It seems there will be heavy rain in the evening.  You had better take an umbrella with you.
• You had better study well.  Otherwise you cannot catch up with other students.
• A: Had we better leave now?
• B: Yes, we had better leave now.
• A: Are you going out this evening?
• B: I had better not .  I am expecting a guest.
• They had better surrender to the police before being caught.
• You don’t look very well.  You had better not do heavy work.

HAD BETTER and SHOULD compared.

‘Had Better’ is similar to ‘Should’ but not exactly the same.  We use ‘Had better’ meant for only a particular situation ( not for things in general).  But should is used in all types of situations to give our opinion or to give advice.  Also, with ‘Had better’ there is always a danger or a problem if you don’t follow the advice.  ‘Should’ only means  ‘ it is a good thing to do’.

Compare:

• It’s a great film.  You should go and see it. (but no danger, no problem if you don’t).

BUT :  * The train starts at 8.30.  It’s already 8.20.  You had better go now or you will miss the train. (here  if you don’t follow the advice, you have a risk of missing the train)