Would Rather
We use "would rather" to express a preference. It means the exact same thing as "would prefer to".
Subject prefers to do something (Same Subject)
Use "would rather" + base verb.
I would rather stay home than go out. She would rather drink tea.
Subject prefers someone ELSE to do something (Different Subject)
If the person preferring is different from the person doing the action, you MUST use the past tense for the action.
I would rather you stayed home. (Not stay) He would rather we didn't talk about it.