Civ4 can be played in very different ways, so I'd say it's important to be perceptive of what she likes and what she doesn't. Some players like to be in control of an army and using it (and thus might enjoy being taught things like a Quechua rush early). Others, including The Woman Of My Dreams (tm), play the game mainly for the atmosphere and don't want to be bothered by wars (so they'd be more interested in finding out which cool buildings you can build and how their effects tie together). Some players want a challenge, others just want a bit of fun in a quasi-historic setting.
My personal recommendation would be to not overdo the teaching. Let her experience the game for a while and see what fascinates her most - the military units? The diplomacy? Building the biggest cities? Having a happy population? Then focus on that aspect of the game, while slowly introducing the others over time.
One of the most important things that new players (and Civ teachers
) should realize, imho, is that the game is perfectly enjoyable without understanding everything about it. There are appropriate difficulty levels for each playstyle. So new players shouldn't despair when faced with the game's complexity - they can ask when something seems important, but can safely leave things for later just as well. And teachers probably need to strike a balance - helping where it's needed and/or appreciated, but not disrupting the "student's" enjoyment by bombarding him/her with too much information at once.