This is a bit of  a difficult topic.  The learner is expected to sharpen his concentration more on the structural nuances than practical examples.  In this case,  be thorough with the structural rules first and work out as many examples as possible.  This usage is specially applicable when you want someone to do something with the connotation of showing your preference.  In this structure we use the past( i.e came, did, did not, asked, knew etc) but the meaning is present or future and NOT past.

COMPARE.

• I would rather cook the food.  ( here the speaker shows their preference of cooking the food.   Implied alternative choices are there of which the speaker shows their choice/interest.  Note that after ‘Would rather’,  the root form of the verb is used.)
• .
• I would rather you cooked the food.  Here the speaker shows their preference that they would like the other person/people to cook the food.( Note that after ‘Would rather’, the past form of the verb is used)

EXAMPLES.

• A:  May I go out now?
• B:  I would rather you didn’t( go out now).
• A:  Would you rather John came to see me?
• B:  Yes, I would rather John came to see you.
• B:  No, I would rather John didn’t come to see you.( i.e if the sentence is in the negative.
• A:  Shall I stay at the hostel?
• B:  No, I would rather you came with us.
• A:  Shall I tell her the news?
• B:  No, I would rather she didn’t know the news now.
• A:  Do you mind if I smoke?
• B:  I would rather you didn’t.( i.e didn’t smoke)
• A:  How will he go, by car or bus?
• B:  I would rather he went by bus.
• A:  What shall I give the baby? A cup of milk or tea?
• B:  I would rather you gave him a cup of milk.
• A:  Shall I take the baby to the garden or to the cinema?
• B:  I would rather you took him to the garden.
• A:  What shall I buy for you, a pen or pencil?
• B:  I would rather you bought a pen for me.
• A:  Shall I inform him the message now?
• B:  No, I would rather you didn’t inform him the message now.