What is the correct truth table for ~p^~q?

This symbol - ~ - is the "not" symbol, which means the opposite.  So I think were given values for p and q?  If so, you just reverse the p values to get ~p (true becomes false or 1 becomes 0 or yes becomes no).  
This symbol ^ is the "and" symbol.  That means that you need to figure out if both ~p and ~q are true.  If so, your result is true (or 1 or yes, depending on which the problem uses).  Otherwise, your result is false (or 0 or no) for each corresponding ~p and ~q value.