Rulebook

USA Swimming rules, in plain language.

Freestyle

Any stroke is allowed except in IM/medley relay, where freestyle means anything other than back, breast, or fly.
Some part of the swimmer must touch the wall at every turn and at the finish.
Swimmer must surface within 15 meters of the start and each turn.

Backstroke

Start in the water, facing the wall, with both hands on the gutter or starting grip.
Must stay on the back (past vertical toward the back) at all times except during the turn.
On a turn, a single continuous turning action is allowed once one hand touches; you may rotate to the breast.
Must surface by 15 meters off every wall.
At the finish, touch while on the back.

Breaststroke

Stroke cycle: one arm pull, one leg kick, in that order. Hands push forward together from the breast.
From the start and each turn, one arm pull-down to the thighs and one downward butterfly kick (during the first arm pull) are allowed before the breaststroke kick.
The head must break the surface during every complete stroke cycle.
Touch turns and the finish with both hands simultaneously and separated.

Butterfly

Both arms must recover forward over the water simultaneously.
Legs and feet must move simultaneously; alternating (flutter) kicks are not allowed.
Touch turns and the finish with both hands simultaneously and separated.
Must surface by 15 meters off every wall.

Individual Medley & Relays

IM order: butterfly, backstroke, breaststroke, freestyle. Medley relay: back, breast, fly, free.
Each leg must follow the rules of that stroke.
Relay exchange: the outgoing swimmer's feet must remain in contact with the block until the incoming swimmer touches the wall.
False starts result in disqualification.

Meet Conduct

No swim aids (fins, paddles, snorkels) in competition unless specifically permitted.
Report to the starting blocks ready to swim when your heat is called.
Unsporting conduct, including interference with another swimmer, results in DQ.
Officials' decisions on stroke legality are final at the meet.

Summary only. For the authoritative ruleset, see the current USA Swimming Rules & Regulations document.