Seconded. This seemed outrageous and unthinkable to me before I was in grad school; now that I've been to grad school, I recognize it as obviously true.

Work your way up to emailing / calling them, but an introduction from a professor that likes you will go far.

Well-known professors get cold-emailed pretty frequently by prospective students, and are largely ignored. An introduction from a professor that likes you, in a related field of study, will get you pretty far.

Of course, you won't get those introductions without having a professor that likes you; the easiest way to get a professor to like you is to demonstrate interest, and start to build expertise, in the field you want to do work in. Start reading papers, ask your professors questions about research, or just pointers to relevant research. If you want to do math or CS or theoretical X, make serious attempts at solving interesting problems. If you're in a lab science, ask to help with relevant experiments at your university.

I did not do these things when I was an undergrad. Doing them would have made a serious difference; I've seen that difference in grad students since then. If you seriously want to do graduate research, this stuff is at least as important as your grades. It's good practice and good signaling.