This tip is a problem I see quite often. Here’s a quick way to know which to use, and when.
Who’s: This is a contraction for who is or who has.
Example: Who’s coming over for dinner?
Whose: This is the possessive case of who or which.
Example: Whose house are we going to for dinner?
Here’s an easy trick: If you were to replace it with who is or who has, would the meaning change? If no, you want who’s. If yes, you want whose.