You can ask your professors questions that aren't related to that specific class. You can ask them for guidance re: next steps you should take to pursue this course of study. Howdoyoufeelmeow has some good suggestions. Even just saying hello and chit chatting after class about some point someone made, perhaps walking with them to their next class.

I got to know mine by speaking up during class, going to extracurricular events and mingling, asking questions related to their field of expertise. I helped one professor clean her office in exchange for her supervising 6 credits worth of independent study Is there a lounge space for your program? I am not sure what you would call it, but my university had areas set aside for different programs where people could get together to study or talk or whatever.

Another idea is to get a small group together to work on a research project with the professor's guidance. That can be a fun way to get published and get to know your classmates and professor at the same time.