If you want to play with friends in the same house without using the official online servers, you can use the developer console to host a local match.

It is important to note that in the standard retail version of the game, Combat Training has a separate progression system from the online multiplayer. You will still "level up" and unlock weapons, but this progress stays within the Combat Training environment. Playing Without an Internet Connection

One common hurdle for PC players is Steam’s requirement to be online. If you are in a location without internet, you must use Steam’s Offline Mode. Open Steam while you still have an internet connection. Go to the Steam menu in the top left and select Go Offline. Restart Steam in Offline Mode. Launch Black Ops 1.

This method is more technical but allows for a pure LAN experience without the lag associated with online play. Using Community Mods for a Better Experience

The ability to unlock all items immediately for offline play.