In college classes of large size, what's the best way to learn and develop a relationship with the professor?

Good question. There are a few ways to approach this. One is to prepare at least one good question ahead of your lecture to ask your professor so that he/she knows that you have indeed read the material and looking for deeper insight and understanding of it. You can mention your name prior to asking the question, so that he/she can associate your name with your face. You can also send questions to the professor via email.

Also, you can seek face time with your professor during any office hours made available to students.

Additionally and most importantly, study hard and do well in the course ... your excellent work will not go unnoticed by your professor. You definitely can do this!

I hope the above helps.

This may seem a little cheesy, but I would always go up to the professor after class on the first day and introduce myself. I would tell him/her that even though the class was large, I wanted to personally introduce myself. I would also try to drop a little fun fact or item to help them remember me. That helps with the above comment about stopping by during office hours as well - because then they will know you (or at least be aware of you).

Sit up front, participate in class, and communicate your concerns with your professor frequently. Visits during office hours is a great idea.