Blue,
I live up by Payson. If you want to get together some time PM me. There are lots of places to fly fish in Arizona. The Salt is the closest to you if you live in Mesa. You can go down to Game and Fish on University East of Bush Highway/Power Road and get some information there. Also, there are numerous "Urban Lakes and Ponds" you can fly fish easily. However, you need an Urban License, if you've not gotten you Az fishing license look into the combination of the two for $53 then you can fish any waters in Arizona with the exception of on the Reservations. Bass Pro, Sportsmen's Warehouse have some good people working there. Ask for Rocky at Sportsmen's he's a good guy and extremely knowledgeable.
Rockthief: I've heard of the book in the past so I now have one on order from Amazon.
Cold: I agree with you also. Get out on the water and wet the line.
Also, you can go to Bass Pro and get some lessons on the casting part. You need someone with experience to give you some pointers for sure. Most new casters hit the water in front of them and the ground behind them.... WRONG!!!! Remember 10 and 2 as on the clock for false casts then about 9 on the cast.
I will be down in the Mesa area this weekend if you want to get together. Like I say, PM me and I will get back with you. We can hit Red Mountain Park or something.