Hi Daniel,
If you are really serious then buy "Backgammon Boot Camp" by Walter Trice. Trice was an actuary so some of this is matchmatical but it starts assuming you know the rules and builds from begginner through to quite advanced. Read and reread. He explains the Ward count but now the Keith count is far more accurate so just google it.
A lot of people recommend "Backgammon" by Paul Magriel but it's old and I rolled out the advanced section (skipping the opening rolls) and found only 72% of the positions were correct. Therefore 28% are wrong.
Next I would buy "501 Essential Backgammon Problems" by Bill Robertie - read and reread.
Next I would look at all the Problem of the Week solutions at this site. These ae done by 2 time World Champion Bill Robertie. Put "Solution" in the search facility here then starting at the oldest print them and understand them. I have had them bound into books.
Avoid playing for money online as there is so much cheating (use of computer Bots).
Buy Extreme Backgammon the fastest and most accurate bot around.
Learn to Pip Count. Walter Trice and most authors try and fail to teach this. I would run screaming from the room trying their advice on pipcounting.
http://www.mindgamescenter.com/ has lots of good cheap articles on various topics but I like the one on Pipcounting (ok, I wrote it so I am biased).
Once you have Extreme backgammon you can buy some group lessons from Stick Rice. They are really good videos for about $25. Well worth it.
Avoid players who say "let me show you an interesting position that came up the other night ..". It did not! It will be a "Proposition" that they have played out many times. They want your money.
Remember to have fun and do not beat yourself up if you lose. No one plays perfectly.
Last edited by Robertie; 11-30-2012 at 11:42 PM.
Reason: Misprint