Congratulations on your first gator sighting!
Like many of the other writers, we too have spotted alligators in most of the ponds at one time or another; enough to realize that one is likely around even if we don't see it. Most of us are excited to see these amazing creatures and watch them safely from a respectful distance.
That said, here is a link to a brochure from the Florida Fish and Wildlife Commission that explains how to live around them safely and how the nuisance alligator program really works. Gators under 4 feet generally prey on fish, frogs and other small animals and are not considered a threat to humans. However, wise people will walk their "other small animals" well away from ponds, whether you see an alligator or not.
http://myfwc.com/media/152524/Alligator_Brochure.pdf