This Edition, Pevear and Volokhonsky (Viking 2001), supposedly renders Tolstoy's Russian more faithfully than earlier ones, which attempted to "soften" him a bit for Western sensibilities. I actually bought this for a class, and my teacher, who reads it in the Russian, simply couldn't praise the translation enough, so if you're determined to read Anna Karenina already, you should probably get this edition.
As for the story, I found that the 800 pages just melted away. Long doesn't mean hard, after all, and I was sorry to see it end, to tell the truth.
The story revolves around seven different people in 1870s Russia. Superficially, it tells how Anna Karenina left her husband for another man, destroying her family, how Stiva Oblonsky ruined his family without leaving it, and how Konstantin Levin courted Kitty Shcherbatsky and they built a new family together.
Although it's enjoyable even on the superficial level, Anna Karenina rewards careful study, revealing intricate structure and interlocking symbolism throughout. Tolstoy thought it was his best work; critics have called it one of the best novels ever written; don't miss it.