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.