Only required once or twice per game, sometimes never at all - but if you want to be even a semi-serious player, you have to learn to count the pips. This is a great introductory article in the art of pip-counting.
"GNU BG" is free Backgammon software that plays a very strong game and can coach you in the correct moves to make when you play against it. This tutorial guides you through from set up to using this software.
This site has been around along time and is popular with players. You can play against other people online here for free. One good aspect is the ability to download the matches you play and analyse them using GNU/Snowie/XG.