First off, let's get to the basics.
To do a LAN you need a high speed internet (cable or DSL are most common). Chances are there is more then one computer in your house, so you will need a router to send the information to both computers. You can either be physicially attached the router using a wire, or you can use a wireless network.
A LAN will allow any computers on the same network to play against each other without going onto battle.net. I hope this helps out.