Who's = who is.
Whose = possessive.
Who's coming to dinner? = Who is coming to dinner? = Correct
Whose shoes are those? = Who owns those shoes? = Correct
Wrong, Wrong, Wrong:
Who's shoes are those? = Who is shoes are those = NO NO NO
Whose going to cook dinner? = Who owns going to cook dinner? = NO NO NO
In short, if you can't substitute "who is" and having it make sense, use whose.