it depends on what platform you are attempting it with. if you are using an xbox360 or ps3, look on your copy of the game box to check and see if it supports "system link" With that being said, most fps "first person shooters" have a system link option in general whether it be on a console or on a PC. The "system link" option allows you to directly connect via ethernet cable to another system without having to go online to do so.
I did some research and LAN is not supported for mw2 on the pc. Which i believe is was pretty stupid of infinity ward not to put that as a feature in the PC version. However i did stumble across some additional info that you may or may not find interesting. post follows bellow................................
how to play Co-op Special Ops (two player scenario missions) privately over LAN (Local Area Network) or with a friend over the internet.
Things you will need:
1. Download and install Tunngle. It will ask to reboot your PC after installation so reboot your PC.
2. Start Tunngle, and create an account.
3. Click on browser on the bottom left of the program to choose the type of game you want to play. Choose ‘Shooter’, and then choose MW2 from the list.
4. Open your Call Of Duty Modern Warfare 2 directory.
5. Unrar the coop.rar file downloaded from the link above, open the folder named "coop" and copy and paste the contents into your Call Of Duty Modern Warfare folder clicking "replace" when asked.
6. Start TCSB.exe and hit refresh. You will now be able to see the servers hosted by other players in the Tunngle MW2 channel, simply hit "join" to join a host. If you are alone or if you want to play with your friend, host a server and tell your friend to join that. (You must be in the tunngle MW2 lobby for TCSB to find hosts).
7. If you joined a host: after the game has loaded, On the main screen before you choose any game mode hit F12 to join the current hosts game.
8. If you host a game: simply set up the game in two player special ops mode and wait for someone to join your game.
I understand that it is only 1 mission but as far as LAN for the pc version of mw2 that is as good as it gets. I hope this helps you to some degree.