Use who's when you mean who is or who has, and whose otherwise.
When should you use who's instead of whose?
Well, who's is always short for who is or who has. For example:
Who's that guy in the red tie?
Who's the actress in Out of Africa?
Who's been a good boy?
The easiest way to explain whose is to say that you use it whenever it would be wrong to say who is or who has. For example:
Is he the guy whose tie was red?
Was it Streep whose career peaked with Out of Africa?
Whose PC is this?
The different uses of these words is illustrated by the following pair of sentences:
Bob, who's normally prompt, was late today.
Bob, whose record is exemplary, was late today.