I learned about distributed computing in the '80s by writing a lot of small client server applications, tearing apart early chat systems, looking at the internals of NFS, etc.

Pick some current distributed system you find interesting and write a simple version of it. You probably can hack together a lightweight dropbox clone pretty easily.

Pick up a good book on network internals. You should find a lot of good information on fundamentals as well as example problems for you to work on.