You can run Steam games in offline mode without an internet connection but it is not exactly obvious how to do so. It is also very easy to "break" offline mode and put steam into a limbo state that can only be fixed by going online again. Here are the steps I used to ensure that my Steam games remained playable in offline mode for the duration of a recent vacation without reliable internet access.
1. The most important thing is to prepare in advance and set up offline mode while you still have a good internet connection. If you simply try to run Steam without an internet connection it will hang for a long time. It may eventually offer you the choice of going to offline mode but don't count on it and don't count on your games being playable.
2. While you still have a good internet connection - log into Steam and check that all of the games in your library are fully up to date and ready to play. Any game that does not have a "ready to play" status will not work in offline mode.
3. Go to the Steam menu (top left hand corner of screen) and select offline mode. You will be given the option of restarting Steam in offline mode. Say yes and test out that your games are playable.
4. Some games (most Valve games) will give you a warning that you are out of sync with the Steam Cloud. Ignore this and just select "Play the Game".
5. You are now good to go. I suggest shutting down the machine at this point and heading off to the great internetless unknown.
6. Steam and its games will continue to pester you about going online. Resist any urge to do this as you risk breaking offline mode and putting Steam into a locked up state that can only be fixed by going online.
7. Do not try to run games that are not installed or not "ready to play"
8. Do not logout out of Steam or try to change to a different user while offline. This will put Steam into that limbo state that can only be fixed by going online. Even if you have multiple user accounts on the laptop do not allow another user to try to log into a different Steam account.
9. Do not try to use any online features of Steam such as Friends. This is obvious I know but a careless moment could put Steam into the dreaded Limbo state.
10. When you get back to civilisation you can use the Steam menu to restart online mode.
That's pretty much it. Enjoy your offline gaming.