I am also fairly new, but I feel like I have been learning very quickly using the tools that I now have. Here's how I got started:
- Download GNU Backgammon. It's free. It will serve to introduce you to the game, to show you how bad you really are, and then to teach you the moves you
should be making to not be so bad.
- Find someone to play live backgammon with. I have a friend who kind of learned the same time as me. It keeps the game fun to play real life backgammon. I also found a small group in Milwaukee that meets once a month to play chuettes. Keeps it fun and a good way to learn...
- Read Magriel's book. "Backgammon" - Paul Magriel. I also just ordered Robertie's "501 Essential Backgammon Problems" as it seems to be one of the most widely-recommended. But I haven't seen received it yet, so I can't give a first-hand review. I bet you could find at least one person on these forums who would recommend it, though
- Before you start worrying about the cube, get a solid feel for checkerplay. I really didn't know what I was doing with the cube until after hundreds of games. Actually, I probably still don't know what I'm doing...