What it does
On a manual watch, turning the crown winds the mainspring via the keyless works (a small set of gears that translate crown rotation to barrel arbor rotation). On any watch, pulling the crown out one click engages the date-setting mechanism (if present); two clicks engages the time-setting mechanism, hacking the seconds hand on most modern watches. Push it back in to return to running. On automatic watches, you typically don't need to wind via the crown; the rotor handles it.
Screw-down vs push-pull
Push-pull crowns click in and out of positions and can be operated quickly. Screw-down crowns require unscrewing first (typically 4-6 turns) before they can be pulled out. Screw-down crowns add 2-3 ATM of pressure resistance and are mandatory on watches rated above 100m water resistance. The trade-off: screw-down crowns are slower to use but vastly more reliable on dive watches and tool watches.
Crown placement
3 o'clock is standard. 4 o'clock (Panerai, some Audemars Piguet) reduces wrist contact for comfort. 9 o'clock ('destro' or left-handed) is rare; designed for wearing the watch on the right wrist. 10 o'clock on the Panerai Luminor is a vestige of the 1936 Italian Navy Marina design. Modern brands occasionally play with placement for design or ergonomics; standard remains 3 o'clock.
Why never operate underwater
Even on a screw-down crown, the crown is only sealed when fully screwed down. Unscrewing it underwater immediately exposes the movement to water through the crown tube. The same applies to push-pull crowns: pulling the crown breaks the seal. Always set the watch on dry land, screw the crown back fully before water exposure. See wiki: screw-down crown.