The first thing to do is figure out how you’re going to do this. Are you going to record your girlfriend and a pianist performing simultaneously, like at a recital, or are you going to record them separately, one after the other?
Are you going to use an electric keyboard, or an acoustic piano?
How much do you want to spend?
Since your girlfriend is a singer, maybe she knows someone with at least rudimentary recording gear. If she’s in school there’s probably a tech that records concerts and recitals that she can hit up for info or maybe even the tech can do a proper recording for a small fee.
Software-wise something cool edit pro should do the trick.
Hardware-wise the 16 bit soundcard in your computer should be OK as long as it has a line input. Mic inputs can be very noisy. What soundcard do you have and what kinds of inputs does it have?
You need a half-decent microphone and (ideally) a mixer or preamp to set the level and output a line signal to your soundcard. A couple of microphones and a mixer can be rented from your local music store.
What kind of room are going to record in?