Who breaks
The lag winner chooses who breaks the first rack; after that the break alternates.
Nine object balls, played in numerical order: you must always hit the lowest-numbered ball first. Legally pocket the 9 — on any shot, even a combination — and you win the rack. Shots are not called.
The short version
The lag winner chooses who breaks the first rack; after that the break alternates.
The nine balls are racked tightly in a diamond, with the 1 at the front (towards the head of the table) and the 9 in the centre, on the foot spot.
You break with ball in hand behind the head string. If nothing is pocketed, at least four object balls must reach a rail or the break is a foul. In addition, at least three object balls must be pocketed or cross the head string (any combination counts); if not, the break is illegal under the three-ball rule (WPA Regulation 16): your opponent may play the table as it is (no push out allowed then) or hand the shot back to you, in which case you may push out. If the 9 drops on such a break, it is spotted.
On the shot right after a break without a foul, the shooter may declare a push out. On a push out you don't have to hit the lowest ball first and no ball has to reach a rail. If there's no foul, your opponent then decides who shoots next.
Legally pocket any ball and you keep shooting. Legally pocket the 9 on any shot except a push out and you win the rack. If you miss or foul, your turn ends; after a miss without a foul your opponent plays the cue ball from where it stopped.
Only the 9 is ever spotted — when it's pocketed on a foul or a push out, or knocked off the table.
After a foul your opponent gets ball in hand anywhere on the table. The fouls are: scratch or cue ball off the table, wrong ball first (the first ball hit must be the lowest-numbered one on the table), no rail after contact, no foot on the floor, ball off the table (only the 9 is spotted), touched ball, double hit, push shot, shooting while balls move, bad cue ball placement, playing out of turn, slow play and the rack-template foul.
Three fouls in a row within one rack lose that rack. For unsportsmanlike conduct the referee chooses a fitting penalty.
The player who broke this rack breaks again.