These positions may be paid, for credit or voluntary, but they are always invaluable experiences. On my campus there is a program in place that allows everyone on campus, undergraduate and graduate to do research. You can start at the beginning of your freshman year if you find something that you are interested in and faculty will support you. Your campus may or may not have a program like this in place, some schools only let graduate students initiate projects, but many need assistants. On many campuses, instead of being called research projects, they are listed as independent study, and you need to be aware of the specifics to your campus and major when you seek that information.
Research can consist of doing almost anything.
It can be in your major, minor or something you are just curious about. The best way to get a full experience is to actually do something you are interested in, otherwise a semester or year of research is like torture. Currently, I am researching paper. It doesn't sound very interesting or prestigious, but paper is actually something I am interested in. I work with a group of people who are exploring alternatives to virgin paper on campus.