In order to play L4D on a LAN you must have the following:
At least one valid copy of L4D (technically none but I don't feel you should pirate this game) A LAN (duh) Enough computers for everyone to play on An internet connection (you might not need this but I have not tried)
Install L4D on each computer (you can use the same account). Create a desktop shortcut and append -console to the target in its properties. Run L4D on each computer. Now type in the console for each "bind F12 toggleconsole" without quotes. This will set F12 to bring the console up (or put it away). On the hosts computer type "sv_lan 1" without quotes and then "sv_allow_lobby_connect_only 0" without quotes. Now type "map" without quotes and without actually entering the command. You will see a small drop box with a list of commands and maps, use the up and down arrow keys to select the map you want and then hit enter. The map should load on the hosts computer. Now have each of the other players type "connect xxx.xxx.xxx.xxx" where xxx.xxx.xxx.xxx is the IP address on the LAN. Each will connect and there you go. Rinse and repeat for loading other campaigns.