In the header file, you need to tell the compiler that string is
in namespace std

Code:
 class addressType
{
public:

	addressType(std::string theStreet, std::string theCity, 
                                     std::string theState, std::string theZipCode);
	addressType();

private:
	std::string streetAddress;
	std::string city;
	std::string state;
	std::string zipCode;
};
(also, you should pass by const reference instead of by value in
the constructor).