How to Play 8 Ball - The Basics
The Object of the Game
The object is pretty simple. Sink your balls to get to the 8 ball, then pocket the 8 ball to win. One player is solids (balls 1-7) and the other is stripes (9-15). We'll get into how to choose who's solids and who's stripes a little later.
Rack 'em Up
Racking the balls really isn't as complex as people make it. Some people insist that the balls have to be "boy/girl" with solids and stripes alternating in order, but that really isn't true. Put the 8 ball in the center, a solid on one corner and a stripe on the other corner and you're good to go. When you rack 'em, make sure that the rack is tight and that the front ball is on the foot spot.
Usually the one who wins the opening lag gets the first break. After the opening break, breaking order varies based on the rules you set up at the start. The most common breaking orders are either alternating or loser breaks. Be sure to set the break rules BEFORE the start of a game. A couple other things. If you scratch on the break you don't automatically lose, the other player just gets ball in hand behind the head string. Likewise, if you sink the 8 ball on the break, you don't win. You either spot the 8 ball or re-rack.
Called Shots and Slop
Traditionally, 8 ball is a "call shot" game. That means you have to choose the pocket where you're shooting before taking your shot. If a ball goes into a pocket, but it isn't the called pocket, that would be the definition of slop.
Choosing Your Ball Group
The way you choose your ball group is fairly simple. After the break, the table is open regardless of whether or not any balls have been pocketed. When a player pockets a called ball following the break, that's when you choose whether you're solids or stripes.
Winning the Game
This one is easy. Clear your balls. Once your balls are clear, call the 8 ball and sink it. The first one to do so wins.
Losing the game
There are a few ways you can lose beyond simply not sinking the 8 ball first. If you foul when you pocket the 8 ball, jump the 8 ball off the table, pocket the 8 ball in the wrong pocket, pocketing the 8 ball when it isn't the legal object ball. These are just the basics as there are quite a few other rules involved with the details of the game. You can find more information on the BCA's website.