Yes a decent AC/DC ammeter will run you about $100, I have the
Craftsman #73756 true RMS +/- 1% accuracy not the best but the price is right. They have cheaper models but 3% accuracy is a travesty. I got mine on sale for $70 8)
If you can't afford one of those, then your next best bet is to hack up an
ATX extension cable carefully so you can put the ammeter inline (I'll assume you already know
how to measure voltage / current) on the appropriate rail.
If you are measuring power, I would take the voltage and current readings concurrently (using a second dmm for voltage measurement) on a per-rail basis, and take an average of five readings or so... ok well you are in a physics class so I can assume you know all the lab procedures as well
If you're time sensitive and need to plot voltage / current / power vs time, why not try a camcorder and a stopwatch, then it is only painful to calibrate the physical stopwatch and the on-screen stopwatch... Ok I'll stop ranting now