At my school, you can actually take a "research internship" course, for credit. They also offer "Independent study" courses, where you're in the lab actually doing research. You actually can decide how many credit hours you want it to be worth, anywhere from 2 hours, where you're in the lab approx. 4-5 hours a week, up to 5 hours, where you're in the lab approx 9-10 hours a week. You can also do research earning cash at my school, but from what i've heard, it's less hands on and more scrubbing dishes, etc. You may want to look in to see if they offer similar courses at your school. If not, they offer plenty of research opportunites at other universities and institutions over summers, etc.
As far as volunteering, I was lucky to "know a guy who knows a guy who knows a surgeon," so I was able to get some really great hands on job shadowing experience that led to a paying gig at a clinic. Best of luck.