Steam – How to Find My Steam ID

As far as I know, you can't do that. If one of you wanted to play single player, then you could possibly set one computer to Offline Mode before starting the game, and then the other person should be able to log in on the other account and play multiplayer, but both of you being online at the same time should not be possible.

Keep in mind, this is technically not allowed. Steam's agreement says you're not allowed to share your account or your games, that includes your fiancee. I don't think they actually do anything about it as long as you're not talking about it on steam chat or their forums. However, you still risk losing your account and all your games when bypassing their rules.

EDIT: As of mid 2014, Steam has released Steam Family Sharing, which enables the sharing of Steam libraries. However, this system does not work on a per-title basis (only during the beta), but rather - If one title is being played, all other titles cannot be played (unless it's the same user that's using the library that is launching the second/whatever-is-after-first program).

Not all games that are released through Steam support adding the version not bought through Steam to the Steam library.

This is the up-to-date list of games that support registering them in Steam. As you can see, it doesn't include Civilization IV.

However, remember you can still add the game as a "non-Steam" game. This gives you the benefit of the Steam overlay, but does not make the game auto-update and does not allow you to download the game from Steam.