In my undergrad at a HUGE university, I had the same problem... I actually talked one on one with a few professors trying to find some guidance/mentorship. I finally found a professor and class I loved (on therapy techniques & theory); one day I just approached him after class and asked if we could meet and talk about issues in Psychology not related to the class per se. We had a long discussion about how I chose the major, what I wanted to do with it (at the time it was research), and how I could get more involved as an undergrad... A few weeks later he set me up with an interview for a research position at a nearby university!
It was really a great step for me and my career. That professor really was instrumental in getting the ball rolling (which at big universities is hard)!
The suggestions here are great:
1 - get decent grades
2 - stand out in class, but not in an annoying way (sit up near front, ask thoughful, relevant questions, do the work/readings, ...)
3 - don't be afraid to ask one or many professors for their guidance/advice (some may not be interested or have the time to meet with you - don't get discouraged)
4 - be your own advocate and look around for opportunities (RA's, TA's, jobs, etc.) in areas you'd be interested in...
Good luck!