You're talking about P2P
Have a look at this its so straightforward and easy to implement.
Test your game on Localhost then LAN then through the internet.
If you plan to commercialize your game you'd eventually want a dedicated server and is also possible to turn your WinBox or LinBox into one through port forwarding on your router. You if decide on the latter you'll want to check with your ISP to increase your UpLoad speed.