The general answer to this is to pay for yourself only. That's my normal way of doing it. However, if you feel you need to pay, make sure (1) you don't make a big presentation out of it, do it very non-chalantly, as though it doesn't mean anything, just a philanthropic gesture and/or (2) you tell her she can get you next time. If you don't do these things, there may be the problem of it coming off as a bit manipulative. The last thing you want is some girl you just met reading into it, which she will undoubtedly do, since she IS female.
Last time I went out with a girl who expected me to pay on the first date I never called her again. Sometimes it's hard to not pay when she just sits there waiting for it because if you guys planned on doing something afterwards, you will either create this tense awkwardness that will spoil your evening, or you'll have to insist she pays and cut off the evening right then and there. Sometimes for the sake of you enjoying the rest of your night, you just go ahead and pay, have some fun doing whatever you want, and never call her again.
