I don't know if this will actually help you, but...
I was actually required to complete a research project in high school, so that opened the door for me. I found a behavioral neuroscience lab (at the University of Kentucky) that worked with rats, and I loved it (for a while), so once my project was complete, they hired me as a lab assistant, then as a lab tech. I stayed there for over six years (not continuously, since I was attending college out of state for three of those years; more like 4 years' worth of work).
Oh, actually, I had two more experiences:
When I went off to college, I worked with one of my above PI's former grad students (so more rats). However, almost the only things available for me to do were sweeping the floors and cleaning operant boxes. I was, however, able to receive course credit (1 hour) and pay ($6.50/hour) for my time. This was through Biology Research Experience for Undergraduates (better known to some as BREU). I am not certain if this was a school specific thing or if it's a nationwide program, but it might be worth looking into.
I also worked in a social psychology lab for one semester. I got this position from a student mailing list post (it may have been just for psych students) asking for students to help with a dissertation project (for class credit). I actually responded to the list and was told they were full. Then a month into the semester, they contacted me because someone dropped out. Hooray for me! It was very interesting to see the human side of research.
Well I mean it's a little bit abstract to just say "I want research experience to help my application."
You should really figure out if you're actually interested in some area first, read up on profs you might be interested in working with and go into their labs with some knowledge of what they do in general. I don't know any professor who would bother wasting time and resources on a student who says he or she just wants "research experience."
edit: then again, I'm in a lab that gets a lot of undergraduate interest and my PI can afford to be very selective about who she takes and retains. maybe others are different...
Yes, I agree 100%. My lab and our colleagues' labs were always flooded with undergraduates who wanted to work in them (for credit, too, not pay, which meant they were not interested in paying student assistants, fyi; eta: sometimes they were looking to hire student workers for the summer), and they got their choice of the best, brightest, and most motivated to be there. They were definitely for students who at least
My advice echos nyanko's. Look at different faculty webpages in different departments, and find out who's doing something that sounds interesting. Then read some of their papers and see if it still intrigues you and if you could see yourself doing that for a bit. It would also help talking to the prof if you have some idea of what they do.
And here's another thing: as a student or even a low-level assistant, it is very likely you would be doing a lot of grunt work. For example, in our lab, our undergrads did a lot of new rat handling, rat weighing, food weighing, etc. Which is
boooring. But they learned a lot about how our lab worked and what real research is like (even if they couldn't do some of it). They also were able to participate in running the experiments, but they mostly did the lower-skilled, repetitive stuff.
So make sure you want experience in that area, otherwise you might just become resentful of your "evil overlords." I'm not saying it's guaranteed to be like that everywhere (I think a lot of smaller labs have more interesting opportunities for undergrads), but that was in the neuroscience labs and in our colleague's labs.