Assuming you mean basic science research, first try and figure out if you are interested in a particular topic. For me, it was developmental biology. Every department will likely have a website with the faculty listed and anywhere from a blurb about their research to links to their lab website. There were researchers involved in developmental bio in a bunch of different departments in both my school and the nearby medical school. I e-mailed the professors whose work I was most interested in, saying who I was and what I liked about their work. Soon, I had a positive response, and began work immediately afterward.
Finding clinical research involved a similar, though a bit more convoluted process, where I e-mailed various chiefs about shadowing under a department in the medical school's teaching hospital and later asking the chief if there were any opportunities.
TL/DR, every department will have a website, listing researcher's work and contact information. E-mail them until something good happens.