I'm trying to make a game with a friend of mine in the summer, and if possible would like to keep the option of having multiplayer. If I pick up a book, will the learning curve for winsock be small enough to start programming some multiplayer apps within a few chapters?

Learning curve for winsock API is negligible (unless you're doing cross-platform networking).

However learning the networking concepts is a much bigger task.

Winsock is just an implementation of the TCP/IP stack, and even that is just description of packets and low level mechanisms. As pointed out before, sending bits and bytes is the easy part. It takes considerably more effort to use networking effectively.

Arbitrary

You should be familiarized with socket IO easily especially because games rely on UDP.

Kuphryn