Here's the super simplified version-
Each player gets one of the pockets at the bottom of the table.
The object of the game is to pocket 8 balls in your pocket before your opponent.
When breaking, instead of busting the rack wide open, players will use a safe break that drives a few balls to their side while leaving the cueball on the opposite side of the rack to protect them.
The ball numbers are meaningless, and slop counts, so making a ball in your opponent's pocket counts for them, unless you scratch on the same shot. (more on this below)
To be a legal shot, a ball must contact a rail after the cueball contacts an object ball.
Failure to do this is a foul, which results in one of your previously made balls being pulled up and spotted.
If they don't have a ball to spot, it is possible to "owe" a ball, and have a negative score.
A foul also results in any balls made on that shot also being spotted, so sometimes a player will intentionally make a ball for their opponent and scratch, which causes that ball to come up at the expense of one of the shooter's own balls.
Despite the pretty simple rules, the game has the ability to get amazingly complex, and great one pocket shooters tend to be very creative on top of being strong bankers and position players. Other people have also mentioned onepocket.org, which is a great resource with tons of information if you can get past some of the crusties that inhabit it.
It's a fantastic game, give it a shot sometime!