For books, I’m not familiar with the one Ard recommended, but the LL Bean Fly Fishing Handbook by Dave Whitlock is very good at about 14 bucks. For a few dollars more though you might want to go for LL Bean’s Ultimate Guide to Fly Fishing. It's a compilation of all 3 LL Bean intro fly fishing books by Dave Whitlock (the LL Bean fly fishing handbook) but includes the other 2 by Dick Talleur (fly tying handbook) and Macaulay Lord (includes the handbook on fly casting) about (16 bucks)
Amazon.com: The L.L. Bean Ultimate Book of Fly Fishing (L. L. Bean): Macauley Lord, Dick Talleur, Dave Whitlock: Books
For fly casting, rather than a book, I’d HIGHLY recommend this DVD by Joan Wulff (about 22 bucks). The DVD will give you a much better sense of the mechanics--- trying to read instructions and convert it into movement will make your head explode. The other thing the DVD does is that it helps to reinforce the notion that fly casting is all about the timing rather than brute strength – Joan Wulff is pushing 80+ years old and is 90lbs soaking wet.
Amazon.com: Joan Wulff's Dynamics of Fly Casting: From Solid Basics to Advanced Techniques: Joan Wulff, Jeff Pill: Movies & TV
Three other things I’d do:
1. Browse through the search feature to see if there are any local chapters of Trout Unlimited or clubs affiliated with the Federation of Fly Fishers near you:
Council/Chapter Search | Trout Unlimited - Conserving coldwater fisheries
Locate a Club
Joining a group can take years off the learning curve. You’ll get help with casting, learn where to go, how to info, be able to try out different gear on the lawn before meetings, get some mentoring from more experienced folks and go on group trips to local waters and meet some new fishing buddies.
2. The internet is your friend. Google “beginning fly fishing” and “fly fishing 101” for some helpful free info on getting started. For fly casting, google “tight Lines fly casting youtube” for a 3 part series of basic vids. Another site is Sexyloops - the best fly fishing and fly casting instruction seven days a week
for tons of info and vids on fly casting. (Just don’t type in the url at work because of the name of the site. You might get a visit from the HR folks.)
3. And last but not least, browse some of the FAQ’s and past threads on this forum and ask questions here too. You’ll get a ton of advise, there’s a lot of helpful folks here.
Good luck and have fun!