Sheee-it. Look into the archives for posts from me, MrMyke, or Dances With Possums.
And buy the book "Fly Fishing the Texas Hill Country" by Bud Priddy -- can find it at bookstores around town, and for sure at the Austin Angler on Congress at about 3rd street (upstairs). My suggested rivers to hit -- San Gabriel, Llano, Blanco, Guadalupe.
There's much more info out there -- we ought to post a fly-fishing primer and just refer people to that.
Blanco and Llano have some great fly fishing, but make sure you are aware of all the rules in Texas (e.g. where you can park your vehicle, wading, etc.)
Austin Angler does fly fishing leason on town lake on Saturdays I believe. They can give you the low down on what you need and where to fish. Also Orvis is another store up by the gateway theater. They have lots of stuff and people that know what there doing as well.