The answer is not too easy. If you are both on the same home network (in your house) then we call that LAN (Local Area Network) and you may get your IP Address:
in Windows, open a "command prompt" and type:
ipconfig
The line with the words:
IP Address: xxxx
contains you IP Address (for each computer that you run it on)
For Internet Games, its best to use Mega-Glest since it offers master server support (which helps people find each other to play internet games)