You can use "prefer to (do)" or "prefer -ing" to say what you prefer in general:

• I don't like cities. I prefer to live in the country OR I prefer livingin the country.

Study the differences in structure after prefer. We say:

• I prefer something to something else.
• I prefer to do something rather than (do) something else.
• I prefer doing something to doing something else.

•  I prefer this coat to the coat you were wearing yesterday.
•  I prefer driving to traveling by train.
but • I prefer to drive rather than travel by train.
•  Ann prefers to live in the country rather than (live) in a city.

Would prefer (I'd prefer...)

We use "would prefer" to say what somebody wants in a particular situation (not in general):

•  "Would you prefer tea or coffee" "Coffee, please."

We say "would prefer to do" (not "doing"):

•  "Shall we go by train?" "Well, I'd prefer to go by car. (not "I'd prefer going")
•  I'd prefer to stay at home tonight rather than go to the cinema.

Would rather (I'd rather...)

Would rather (do) = would prefer (to do). After would rather we use the infinitive without to.

Compare:

• "Would you rather have tea or coffee" "Coffee, please."

The negative is "I'd rather not (do something)":
•  I'm tired. I'd rather not go out this evening, if you don't mind.
•  "Do you want to go out this evening" "I'd rather not."

Study the structure after would rather:

•  I'd rather stay at home tonight than go to the cinema.

I'd rather you did something

When you want somebody to do something, you can say "I'd rather you did something":

•  "Shall I stay here?" "I'd rather you came with us."
•  "Shall I tell them the news?" "No. I'd rather they didn't know."
•  "Shall I tell them or would you rather they didn't know?"

In this structure we use the past (came, did etc.), but the meaning is present or future, not past.
Compare:

•  I'd rather cook the dinner now.

but • I'd rather you cooked the dinner now. (not "I'd rather you cook")

The negative is "I'd rather you didn't...":
•  I'd rather you didn't tell anyone what I said.
• "Do you mind if I smoke?" "I'd rather you didn't."