I'm lazy right now so I will just give you a general example you can use. If you are going to overload + then you might as well overload += as well because you can use the += in your +.
If you're not referring to the string class in C++, but character strings in general, an easy approach would be declaring a new cstring, copying the first string into the newly created cstring, then concatenating the latter with the second string, and finally returning the resultant cstring. All within the body of the operator. Functions that might help, strncpy(), and strcmp().