I started my research with the cardiology division at my school between first and second year. Our school offered a stipend to student's who did research for 2.5 months over the summer. I continued my research during second and third year as well. It is difficult to fit in research with classes but if youre motivated and can manage your time well, then it can be done easily.
I would recommend trying to do clinical research rather than basic science research for a few reasons. A lot of clinical research can usually be done in a relatively short amount of time. For example, I did a retrospective review of 100 echocardiograms and collected data in a week, analyzed it in a week, and took a month or so of writing the paper (it took time to get it reviewed by the doctors and to change the revisions). Basic science research takes much longer a lot of times because of all the lab prep time. Obviously youre not going to be able to do a randomly controlled drug trial with a 5 year follow-up and publish it in NEJM while in medical school, but there are plenty of things that are not as mainstream that are of interest to several of the journals specific to a certain specialty or an area of a specialty. For example, there are several journals dedicated to only echocardiography and others that are limited to cardiology in general. Also, clinical research often involves learning a skill that will help you later, whether it be interpreting lab tests, talking to patients and performing physical exams, reading echocardiograms or xrays/CT/MRI, etc. Also, clinical research will get you to form a close relationship with your mentor who will often have close ties to other people in the field at other institutions. This will allow you to get a foot in the door when applying to residencies outside of your medical school. Any more questions mocheese, please let me know.