Easiest way would really be to get a router, they are usually set to be a DHCP server by default.
Turn both rigs off, plug the router into the net connection, plug both rigs into the router, turn both back on. Might have to tell the router how to access the net connection as in user name and password.
After that you can add as many computers as you have ports.
Cable/DSL routers cheap these days.