The Rules of the Game
Your objective as expanded upon in the 8-ball rules, is to pocket your set of object balls numbered 1 through 7 ("lows" or "solids") or 9 through 15 ("highs" or "stripes") before pocketing the 8-ball on a call shot.
Calling pockets allows flexibility--whether a ball goes straight into the pocket, zooms around before sinking or flies through the air to the hole like a basketball, you retain your turn.
Make an open break, smashing the balls apart. Your turn continues if a ball is pocketed on the break, if not, your opponent starts their turn.
The fairest way to proceed is to have an open table despite what has been pocketed. Even if you've sunk three solids and no stripes, you must make a call shot after the break to ensure solids.
Once your set is determined, you must "play clean" hitting an object ball, one of the balls from your set of stripes or solids, first on any subsequent stroke. Failure to strike your set first (or striking one cleanly followed by subsequent failure to drive at least one ball into a pocket or rail) yields ball-in-hand to your opponent.
Ball-in-hand is awarded following any cue scratch. With ball-in-hand one measure designed to speed play, a second is that object balls illegally pocketed stay down and are not returned to the table. Technically a player could use their turn to push an opponent's ball straight into a pocket!
BCA rules, which pave the way for enjoyable play, stipulate that a scratch on the 8-ball is not a loss of game unless the 8-ball pockets on the same shot. (This unusual rule was set to end long defensive struggles where players were afraid to disturb an 8-ball close to a pocket.)
Pocketing the 8-ball in the wrong pocket (different than the called pocket) or on any stroke before your set is cleared is an immediate loss of game.
Consider classic 8-ball strategy next, few of your opponents will!
For decades, 9-ball has been the darling of televised pool for its explosive open break open break and pocketing action.
9-ball is a rotation game. You shoot at the lowest numbered ball on the table, with the caveat that if the 9-ball falls on any shot anytime, even on the break, it's a win!
The balls numbered one through nine are racked in a diamond shape, the 1-ball in front (so the player may hit it as proscribed first without added difficulty) and the 9-ball in the center (for added protection from pocketing on the open break). Beginners forget to hide the 9-ball in the center. If the nine is moved to another position, a pro could sink it on the break most every time to win!
You must hit the lowest numbered ball first with the cue ball. Following that hit, one of the ten balls on the table must touch a rail or sink in a pocket or your opponent receives ball-in-hand. Good players always have an eye to pocketing the 9-ball early for the win.
These are the rules in a nutshell but there are warnings ahead as excellent 9-ball takes much time to learn. 9-ball is a shark pool where hustlers find victims in abundance. Typical rule additions include the "Three Foul Rule" where three fouls or scratches on three consecutive turns end the game. Of note, the rule is enforced only if the opposing player has verbally announced when two fouls have been "achieved" before the third infraction is made. A skilled hustler easily positions the balls to make his prey foul three times and lose.
The "Push Rule" allows the incoming player (following the break shot only) to shoot the cue ball anywhere without touching the lowest ball for a safety or defensive play. The other player may accept the new position or force the person who made the push to shoot again and attempt a regular shot. Again, the hustler is well placed to start hiding the cue ball immediately.
Information above referenced and provided by http://billiards.about.com