It has always seemed to me that the art of fly fishing was made out to be much more difficult than it is, probably to keep people off the streams heh, heh. There are a million books out there (now videos) that show just how you should do it. I think it causes people to overthink it and frustration sets in. A million years ago I jumped in - looking back now it wasn't that tough - I just made it that way.
Take a 1 day class at any fly shop.
Buy an inexpensive 4/5/6 weight rod/reel. They are everywhere. My first fly rod was $65 at Cabelas and I traded a pair of ski boots for a reel.
FOR TROUT -
Get a used copy of the Orvis Flyfishing Guide and Tom Rosenbaurs (sp?) Prospecting For Trout.
Don't worry about matching hatches and all right away. Tie on a #16 Hendrickson dry (or whatever the guy at the shop tells you) and go start casting.
Trout doesn't want to fight the current, but he wants to have food sliding by at all times. Find spots that break the current but where the trout can hang out and watch stuff drift by.
Cast to these spots.
Catch your first sizable fish (10") and you'll either be hooked or not. If you're not, put the rod over the fireplace in the den and the books look good on a coffee table.
If you are hooked, be prepared. It is very difficult to find a better way to spend time than on a fall stream when the leaves are turning and the fish are hungry.
Bass, pike, salmon and everything else are out there for you. I love casting for rock bass on a 3 weight rod.