In general, pool play will be governed by the rules accepted by the Billiard Congress of America.  The complete specification can be found here: BCA Pool Rules -- in particular Sections 1, 3, & 6.

There are, however, a few rules that deserve highlighting:

  • Players must call "ball & pocket".  That is, on each shot you must declare which ball you intend to sink and in which pocket it will go.  As long as no other rule is violated (e.g. hitting your opponents ball first), it doesn't matter how the ball gets there.  If you were intending to hit it straight in and it hits 22 rails on the way, it's still a legal shot if it goes in the right pocket.
  • No balls (other than the cue ball) ever return to the table once pocketed.  You lose your turn if a ball was pocketed illegally, but the ball stays down.
  • All fouls, after the break, result in "ball in hand" anywhere on the table.  The notion of having to play a ball from behind the head string only applies during the break.
  • In general, on each shot, the player must hit one of his own balls first.  Then, either one of his balls or the cue ball must touch a rail (or be pocketed).  Otherwise the shot is not legal and his opponent gets ball in hand.
  • Scratching when shooting the 8-ball is not an immediate loss unless you pocket the 8-ball as well.