From Leeds you could go hop on I-59 and head up to the Nantahalla or the Ocoee, or any of the other great whitewater places a few hours away. they'll have classes and stuff for beginners. I think there are also local canoe clubs (Cahaba Canoe club, Huntsville Canoe Club?) and other groups that you could meet kayakers to hook up with locally to run the Locust Fork, Mulberry Fork, and other rivers with.
At this point, somebody will usually chime in and tell you that MountainBuzz is only a western site, but plenty of Buzzards started off in the Deep South know the rivers down there, and pointers and tips aren't geographically constrained.
Have fun, be safe, and don't go solo!
Nothing in the world is more yielding and gentle than water. Yet it has no equal for conquering the resistant and tough. The flexible can overcome the unbending; the soft can overcome the hard. - Lao Tse