Welcome to the life long addiction of fly fishing. The best advise given so far was to look into joining your local club. It’s cheap and the absolute best deal out there for the beginning fly angler…$35 annual membership year with a one time $10 initiation fee. It looks like a very active club with outings every month to a different water in your area, as well as other activities. It also looks like it has a very good mix of people…young, old, male and female.
You are very lucky that you have this resource available. Take full advantage of it. Don’t feel like you need to be an expert to join a club. These clubs are there to help new fly anglers and keep them in the sport. They will help you learn proper casting techniques, what flies and when, how to tie your own flies and they can answer all the other questions you’ll have…and believe me, you’ll have a lot and don’t let that overwhelm you. This is a life time sport…meaning you NEVER stop learning new things.
Clubs often have a lending library of books and videos to borrow. With so many books on the subject, people there can point you to books you should be reading when in the beginner stage.
Clubs offer a place to swap flies or where you can find the flies that work for your water and folks willing to share or sell on the cheap their winning creations.
Clubs are good places to find mentors. Clubs offer casting clinics and other how to’s for the beginner, but keep in mind that they offer things for everybody so don’t feel intimidated if you hear stuff you just don’t understand when just starting out. In time you’ll learn all that stuff…even how to build your own fly rods if you want.
Check out their current newletters:
http://www.fresnoflyfishers.org/fly_dope/2009/june_july_2009_fly_dope.pdf
If you don’t want to do the club thing (crazy ;)) then save some bucks and go to your local fly shop and hire a guide, who is willing to teach, for a day OR at the very least take casting lessons. It costs a heck of a lot more than getting this through a club but it’s still money very well spent.
How do I know this stuff? I was where you were, seven years ago. I joined my local club…took full advantage of what they offered along with taking every course and class offered outside the club within a two hour drive.
Now I’m teaching, mentoring and the president of that club…and I can even catch a fish or two. 
I like what Ray said… it’s a life long search to find the fly that works at that moment in time…and that can change in five minutes… have fun!