Find a shop you feel comfortable in, for these shops are an excellent resource. Ideally you need a vest to hold your new flies, some toenail clippers to clip leaders and tippets, a pair of forceps to take the hook out of the fish and some waders so you can get in the water where the fish live. Then you need to learn to tie some basic knots, find a trout stream and get out there. Your first few times on the water should be fun, so don't overwhelm yourself with little details, and believe me fly-fishing is loaded with little details. There is a lifetime of information to learn about fishing, and the basic skills and etiquette, if learned correctly, will give you a lifetime of enjoyment.
Fishing is a lifetime sport.
Once you get comfortable with your basic skills is when the fun starts. You may develop fish fever which strikes at will and might lead you to spend all of your time on the river. Fly-tying and rod building may occupy the slow winter months and insects suddenly become very interesting. One may find they spend good portions of the day gathering specimens from the bottom of rocks so they can anticipate a hatch. Once you get into it, fly-fishing can take you around the country and around the world.