Don't email professors. Go to their office instead and ask them directly. A lot harder to say no.
This doesn't always work and can sometimes lead to awkward situations...
If you are in a "normal" premed situation (decently large school, lots of labs involved in bio, biomedical, related research, lots of premeds, etc), then email will (and should) be your best friend. Unfortunately in most situations, the nature of the game means that there are lots of other premeds just like you: freshmen or sophomore, probably no prior experience in research, you've taken the usual classes that every other premed has taken, super eager, etc. The key to getting into research as an undergraduate (based on my experience which is same/similar to the vast majority of my friends and acquaintances who are also in research) is to write a LOT of detailed, personalized emails to professors at the right time. From my own PI and conversations with other PIs, certain things generally hold true when PIs look for undergrads to fill out their labs:
1) They typically start looking for new undergraduates during large academic breaks or just before a semester starts. So think end of winter-break or end of summer break. You are slightly late with this but that is ok as generally the "interview process" goes into the first couple weeks of the semester.
2) Most known bio, biomedical labs get a BUNCH of emails from undergrads about research. You know how PIs distinguish the ones to interview? They look for thoughtful, personalized, and interested emails about their lab's specific research. No you don't have to have prior research. This means checking out the lab's website, reading some recent papers published by the lab, reading descriptions of what the grad students or post-docs in the lab are working on (in all likelihood, you will working under one of these), and being able to specifically mention things that sound interesting to you or stuff you have come across in coursework, etc.
That being said, this all means that you are going to have to spend some serious time figuring out what your interests are academically. By this I don't mean you have to have your senior thesis plan all worked out or what research you want to pursue as a career all worked out. At the undergraduate level, any kind of hypothesis-driven research done in any lab is equally helpful because its all about learning the scientific process, how patient research is, etc. Go to various department websites, read professor's blurbs about their research interests, pick a bunch and then dive into their specific websites and start constructing those emails and sending them out! I sent out >25 emails, interviewed with 3 labs before deciding on joining a lab (that turned out to be one of my best decisions as an undergrad!) Don't be alarmed if you don't get replies from all of them. Unfortunately many PIs will see emails and ignore them if you aren't a fit or if they don't take any new undergrads, etc. You are simply trying to get a few to reply with an interview or a "discussion."
And I agree with the rest that if your school has a specific program or process where you can get "matched" into a lab, then go through that as it is definitely more established. All this stuff is just general information for a general situation of a first or second year with no experience trying to get into research for the first time.
(He stated there was an upperclassmen he was also considering for the same position, but that he liked my GPA. He also asked me multiple times if I could really be committed for the summer because I was OOS). I started that summer and then applied to continue the research during the semester. I did that until I graduated, and each time I had to reapply the semester before through my department. 
