Actually, alligator season in florida is now through Oct 7th.
Alligators have been hunted legally in Florida since 1988. Permits are issued by lottery (10,006 applications last year for 729 permits). Permit holders may take 2 animals, providing each exceeds 18" (that's inches not feet !) in length. Resident license fees are $250, non-resident $1000.
Firearms other than handheld bangsticks are not allowed. Handheld bangsticks may be used to "dispatch" 'gators held by restraining lines.
A popular hunting method is hand-thrown, tethered harpoon from an airboat at night, hauling the gator in close and finishing with a 12 ga bangstick. I'm told it's great fun - but haven't been lucky enough to win a permit yet.
Details, training manaul, permit apps and lots of other great info at:
http://wld.fwc.state.fl.us/gators/
-ric