Purchase the instructional DVD "Basic Fly Casting  with Doug Swisher" by Scientific Anglers. It is available from the Bass Pro Shops online catalog. This is by far the easiest and most efficient fly casting method around. The DVD makes learning fun and fast.
Also if you plan on fishing for sunfish, purchase the DVD "Fly Fishing for Bass and Panfish with Skip and Carol Morris" by Fly Fish by TV, also available from BPS online catalog.
These instructional DVDs are invaluable!
Next, purchase a starter fly casting combo from Cabela's. Get one that is a 5/6 weight outfit with floating line. This is a good all around weight rod to start with and easy to cast.
Then, practice with the DVDs and soon you'll be casting quite well. I learned to cast with these DVDs and I  HIGHLY recommend the methods therein.
Happy Fly Fishing!

One book that helped me a lot when first starting out was the Orvis Fly Fishing Guide. It covers just about all the bases, but the only real effective way to learn to cast that I had was watching video. In person instruction might help too, but the book didn't help me a whole ton with that. Other than casting though, very helpful. I also have heard about the Little Red Book of Fly Fishing, probably worth a look too. Good luck!

keep an eye out at your local cabelas, they sometimes offer fly casting seminars.

You might want to look up your local trout unlimited chapter sometimes they offer free outings to get more members .

My local chapter here in Wisconsin has one coming up end of this month

The videos mentioned by bass or bass are probobly a very good idea. Also there are a ton of books on fly fishing and some of them are applicable to the beginning fly fisher, I have Fly Fishing for the Complete Idiot which is starts very basic. I also have The Complete Book of Flyfishing by Tom McNally which is pretty comprehensive but I am going to bet the videos listed by bass or bass may be the easiest way to get started.
Speaking of seminars, I went to the casting pool in Balboa Park, San Diego, one time hopefully to get some help with my casting, the instructor never showed and I ended up giving some basic lessons to people. Didn't help my teqnique much but was gratifying much the less. Sometimes actually talking with people is very helpful which makes any seminars you might be able to attend and excellent idea.
I have been in that area, years ago and as I remember, the Jellystone is BIG. I admit I much prefered the smaller streams and rivers in the park, I enjoy the intimacy of the smaller waters.

Thanks to everyone for sharing your advice - I realized after I posted this that there was a post nearly identical to mine just a few days earlier! Anyway, I'm heading to Cabela's after work tomorrow after work so while I'm there I'll check out the videos and books that you have suggested. I'll ask if they have any seminars coming up. There's more than a slight chance I'll pick up an entry level flyfishing outfit while I'm there too.

looks like your cabelas location will be holding product demonstrations on the 13th and 14th. it may be worth checking out. Cabelas also offers thier fly fishing university online. I checked some of it out and it seems fairly helpful plus you get a free fly fishing federaton membership.

I made it to Cabela's tonight and picked up a fly fishing combo. The man that helped me really appeared to know what he was talking about, and I asked if they still held seminars in the Dundee store. He informed me of the demonstrations you mentioned - as a matter of fact, he teaches them!

I learned quite a bit tonight, and my wife and I are going to show up on the 13th. I understand there are additional hands-on classes beginning in May. We'll be going to those too.

sounds like your off to a great start. welcome to the wonderful world of fly fishing. its great that your wife is getting involved also.

Brian

I received a lot of valuable information and techniques after I joined a local fly fishing club here in Central CA about 6 years ago. Our club members are always helping each other and offer free casting seminars on the river to help anyone of any skill. As a matter of fact, next month we're having our 5th Annual Kids Fly Fishing Academy sponsored by the club and operated by club volunteers, like myself and my teenage daughter who was one of the first graduates 5 years ago. So, look for a good local fly fishing club and get involved. We have many clubs in this area and I'm sure you will have a few even where you live.

I really wanted to head out in the back yard and start practicing what I've seen online, but thought it would be best to take some classes first. It would probably be easierfor an old guy like me to learn to cast properly up front than to develop bad habits on my own and try to correct them later.