First of all, don't be yourself! Be somebody interesting instead. Remember, she's dating your friend because he's not an introverted dork like yourself. If you can't entertain her with your own imagination, go with some more banal conversation bits like this one:
You: Did you see that major motion picture that opened last week?
Her: Why yes, I did see that major motion picture. I thought the lead actress performed admirably.

You have to be careful not to try too hard. It will likely show:
You: I especially liked how her struggle against the hyper-dystopian oligarchy contrasted with the thematic interplay of Marxist doctrine and Judeo-Christian mythology.
Her: what

Not only have you lost her in a blur of words you saw in a Cliff Note's once, you've effectively put a halt to the conversation. She doesn't know how to respond. Keep it simple, sub-genius:
You: Her breasts are of excellent proportion and volume. I find yours to be of comparable quality.
Her: Thanks!

That's more like it. It's just as important to earn the girlfriend's trust as it is to earn the friend's trust.