I started fly fishing eight years ago. My buddy Ross thought I needed a hobby other than work and so he dragged me up to Manchester, Vermont for three days of Orvis indoctrination. I fell hard for this new thing, just ask Ann. Heck, the fact that I'm writing this stuff here says something about my passion for this sport.
After the school I fished a bit on my own. It took a month or so for me to land my first trout on a fly. That spring I hired a guide to give me some nymphing instruction. And then I attended my first TU meeting and fished with some very talented anglers who helped me run up the learning curve.
If you're not able to do all that, you're left with figuring it out on your own. Fortunately, there are some professionally-crafted, free online resources to help new anglers through the process.
Orvis Fly Fishing Learning Center. It's hard to compete against Orvis in this space. First, they got the talent (e.g Rosenbauer, Kutzer, etc). Second, they've got the resources to do some pretty slick video and animations. Finally, they've got
New to Fly? It doesn't have the depth of content that the Orvis site has but it covers the basics well. The lessons are more demonstrations than lessons. They show the things but don't explain the "why" behind it. For example, the Overhead Cast Lesson doesn't explain the dynamics of the cast -- rod loading, etc -- but simply shows the actions. For some this might actually be better; less confusing technical stuff. For me, I like knowing why. It helps me better understand what I'm doing. That said, it's got lots of content to cover the breadth of knowledge required to get up and running.
Cabelas Fly Fishing University. It too covers that landscape of things you need to know to fly fish. However, for a large company this offering is weak. There's no video that I could find. A majority of the offerings are text only and are broken down into such small chunks of information that I had difficulty putting them in context. Also, the look and feel of the website reminds me of learning sites from work and that's the last thing I'd like to be thinking about when learning about a hobby. Finally, it seems like they've taken the content out of a book but not a very good one. If you want to learn from a book, I think there are better ones out there.
While websites help I've found that the best ways to learn are to actually fish with people who know what they're doing. Just watching a good angler cast helps you add to your repertoire. Also, lots of fly shops hold clinics that let you get free instruction and tuning. Finally, hiring a guide can be the single best way of improving your technique. Just make sure you ask around for recommendations. There are some guides out there who know as much about education as Cabelas does.
 I thought doing hand crafted emails for work was a hobby. Who knew?
 Not to mention my desire to hear myself talk (or write, in this case)