Seems this already happened, but I figured I'd lend some advice to those of you considering teaching the lady.
The majority of situations like this go bad. I have far too many friends who had their first and only experience with a boyfriend.
So, for those of you who insist.
1. Your girlfriend may cry. Be the most awesome boyfriend ever and some tissues with you.
2. You may see a frustrated side of your lady you have never encountered before. Don't tell her it's easy, simply ask what you can do to make her experience better.
3. Do not bring anyone else with you unless they happen to be an instructor. You will be tempted to leave her and go out with your friends. This is a horrible idea.
4. Do not bring her on the lift for her first run. Make sure she is comfortable walking around on the skis first and practice falling and getting back up with her.
5. Aim low. Tell her that your goal for the day is to get her comfortable taking the easiest chair lift. This should only take her the first 2 hours, but whatever, she will be stoked if she gets on a second lift.
6.If you haven't instructed before, the easiest way to learn to turn is for you to ski in front of her backwards and tell her to just keep her eyes on you, stay in a wedge and follow you. She won't even realize that she's turning.
7. Make sure, absolutely sure, that you tell her to never ever try to user her poles to stop herself. The list of injuries caused by this is not a happy list.
8. If you occasionally wear a helmet, wear it and do her the favor of renting one. They are usually less than $10, it will make her feel a bit safer and it is best to start good habits straight off the bat.
I do not advocate teaching your lady to ski. I am a huge fan of ski school and instructed for 4 years. I think the absolute best thing you can do is get her equipment with her, sign her up for a morning lesson, spend 10 minutes with her showing her how to get in/out of the skis and walk around. Then leave her for an hour. She will be less nervous if you don't watch. Then when you know there are about 20 minutes left, do a lap of the chair they are on, ski up to her and tell her how awesome she is doing and say you will meet her at the bottom for lunch before you go back up with her. That will make you seem like the most awesome boyfriend ever.