The frame structure
A game is ten frames. Frames one through nine allow two deliveries; the tenth allows up to three. You aim to knock down all ten pins. All ten down on the first ball is a strike; all ten across two balls is a spare; fewer than ten is an open frame. (Full detail in scoring.)
The foul line
The foul line separates the approach from the lane. If any part of your body crosses or touches the lane beyond the foul line during or after your delivery, it's a foul — that ball scores zero, even if you knocked down pins. Most centers have automatic foul-detection lights and buzzers. A foul on your first ball means you reset the full rack and your second ball plays at all ten pins.
Legal delivery
The ball must be rolled or delivered by hand, down the lane, toward the pins. You can't throw it through the air down the lane (lofting a short distance off your hand is fine and normal; hurling it is not). Two-handed delivery is completely legal and increasingly common at the highest levels.
Legal pinfall
Pins count when they're knocked down by the ball or by other pins. Pins do not count if they fall because of a foul, if they're knocked down by a ball that left the lane and came back, or if they're touched by the rake (the sweep bar) before being counted. If a pin wobbles but stays standing, it stays — even if it's leaning.
Dead ball
A ball can be declared dead and re-rolled in certain situations: a pin was missing from the rack when you bowled, you bowled on the wrong lane, you were interfered with during your delivery, or a pin moved before the ball reached it. A dead ball doesn't count and you bowl again at a properly set rack.
League and tournament layers
Recreational open play uses just these basics. League and sanctioned tournament play (governed in the US by the United States Bowling Congress) add rules around equipment specs, lane conditioning, handicap systems and substitutions. If you join a league, the league secretary will walk you through its specific rules — start with the handicap calculator to understand how league scoring levels the field.