would rather usage

[vkhu]

I sometimes see people use "would rather + V-ed" but sometimes they use "would rather + V" and "would rather + have PII". It's just too confusing. Someone explain their usages for me please.

[5jj]

'... would rather do/be ...' normally expresses a preference for a present or future situation.

I don't like living in the country. i'd rather live in a big city.
I am bored with this assignment. I'd rather be on the beach.
Do I have to go to Aunt Mary's tomorrow? I'd rather stay at home.

'... would rather have done/been' normally express regret about a past situation:

I had to go to Aunt Mary's yesterday. I'd rather have stayed at home.

[vkhu]

What about would rather + past-form verb? For eg: I would rather you didn't do it.

And while you are at it, mind explaining this one for me: I would rather he had been here.

[5jj]

What about "would rather" + past-form verb? For eg: I would rather you didn't do it.

The 'past' tense form is used to distance in reality the thing wished for. The time referred to is present or future.

And while you are at it, would you mind explaining this one for me: I would rather he had been here.

This is doubly distanced, in reality ('he' wasn't here) and in time (the past)