A great place to play is definitely Gamesgrid, although they have sometimes problems with their client-software. A not so famous, but for Europeans also quite interesting place is VOG2, since the time-zone fits a little better having a job and a family;-)
Learning Backgammon involves playing, playing, playing and reading books and nowadays online-resource like Kit Woolseys GammOnLine. This service isn't free, but you may consider subscribing there, have a look at the demo issue on this site and make up your own mind. Anyway, there is a well maintained collection of links on this site, a good place to start from.
Don't miss Oasya's collection of analyzed matches! Read the masters!
OK, this is title a links-page but don't forget about the books, here my favourites:
| New Ideas in Backgammon, Heinrich/Woolsey | |
| Backgammon, Magriel (hard to find (try A&K Klassische Spiele), a little bit outdated, but Magriel's didactic skills still make it a must-read) | |
| 501 Essential Backgammon Problems, Robertie (Robertie's style of playing is unique, but since he is very successful he cannot be that wrong;-) |
Here is an annotated Match I played on Gamesgrid:
and an exerpt from an other Match