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When getting research experience, it's all about quality and not quantity.
Start by looking at the research page on your schools website and see what labs are working on projects that interest you. Once you have a list of labs you like, look at the papers they have published, you'll want to try for a lab that has a good number of publications or publications in well known journals.
Once you've done that, it's time to contact the professors. Email them saying that you are interested in research and are interested in what their lab is working on right now. Ask if they are looking for students right now (they aren't always looking for students, don't worry, just move on to the next person on your list). If they are, ask if you can interview for the position (some labs are more formal than others, some will see you are interested and say come on in). While interviewing be sure to ask how much you will be doing as a student (you don't want a position where all you do is wash test tubes, but keep in mind that everyone starts out washing test tubes, just make sure you will get to work your way up to doing more work on projects as you get more training).
Once you find a lab that's a good fit, stick with it. The longer you are there the more work you will get to do and the closer you'll get to getting your name on a publication. This is going to look a lot better than hopping from lab to lab, so unless you can't stand the lab you are in hang in there.