How can I begin studying the humanities on my own?

Hi, I am transferring to a liberal arts college next spring and I was wondering how can I start studying the humanities on my own? Should I be reading a long list of books from various disciplines within the humanities and liberal arts?

You pretty much answered your own question. Read books, lots of books. Watch some documentaries too.
Anything you can do to expand your own knowledge. Just keep in mind that there are many Humanities-- Anthropology, History, Art-- and they all break down into sub-fields. If you know the college you’re transferring to I recommend taking a look at their course catalog to see what they over, and which ones you find interesting. After you do that, you can pick material that will help prepare you for your future classes, rather than taking a shot in the dark.

Anthropology is a social science.

Reading books is always a great idea, but randomly selecting books might not get you to the goal you want. I agree with @LiberalCrafts that looking at a course catalog is a good way to start to get a feel for what classes you might want to take. You also might decide on a specific humanities field and do some Internet research to find books in that field’s canon. For example, if you are interested in classic literature, there are some foundational texts in the literary canon that might be good to read. Columbia University’s Core Curriculum is pretty time-honored and the list of books they read is public information. There are also lots of unofficial lists of books in the literary canon; you might also look up something like St. John’s College’s Great Books curriculum and see what they read.