I'm a freshman biomedical engineering major doing pre med. I was very fortunate and I currently have 2 research positions: one is a paid wet lab job doing most of the grunt work for a ph.d student and professor's research project which will hopefully get published and the other is working in the research group of another professor doing biological simulations and computational work; this one is more long term and i can stay on for as long as I want (and my work is satisfactory).
I don't think it's early at all; I'm starting the lab work this semester, continues and finished in the spring and starting the research group work next semester. I would love to get published, which can take quite some time, but I also want to get good experience and have an advantage over other freshman when looking for research next year. Classes are only going to get harder so I figure I better start now and get used to research.
So first thing was I looked in the academic departments in biology and biomed engineering here at RPI and professor's work. I emailed 15 professors, about 10 responded back, 7 said their lab was full and they also don't take freshman, 1 said to contact him next semester, and the last 2 were for the positions I got. I actually had to interview for the paid research position as there were other applicants but I was immediately taken into the other research group.
So I would recommend looking at the work professors are doing, see what interests you and email the professor briefly introducing yourself and stating you're very interested in their work and ask if there's any openings in their lab for research experience (state for next semester too if you want). You should email plenty of professors because a) their labs are probably full and b) they specifically may not take freshman.