depending on how mutch you are willing to spend,Igot into flyfishing a couple years ago and it only costs about $150.go to bass pro shops and get a dogwood canyon outfit it comes with backing,WF fly line and a taperd leader its only 90 doolars and you can spend the rest on flies,taperd leaders,and any other supplies. you might need

Redington crosswater 5 wt 125$ with shipping bought it this summer and got into what i've been told was the easiest fishing with using poppers and have talked to a good friend mine who answered all my questions and taught me to do alot of stuff myself. mostly make my own leaders which get expensive and also sold me flys for 1.25 a piece and they were the ones he uses in the area. i am always looking for ways to do it cheaper and in many ways its easier with fly fishing you can make alot of flys out of some relatively cheap material. I just started attempting to tie with pheasant feathers from the birds i shot this year.

Cost? Depends on you. Many start out with a combo outfit from one of the bigger outlets like Cabela's, Bass Pro, Gander Mtn. etc. Typically around $100.00 will get you an outfit that'll be pre-spooled with line and backing. Decide what fish you'll be after and talk with the sales staff and they'll match you up with the correct weight rod.
You'll need waders if you don't already own a pair. A couple options there. (breathable or neoprene) Breathable are lighter and are best for warmer water, neoprene are heavier and keep you warmer in cold water. Keep in mind there are various thicknesses of neoprene too. Next will be stocking foot or boots. I prefer stocking foot but that'll be your choice.
Next you'll need some flies, again, talk with sales staff as packages of various sizes and flies are common.
Look at a few casting videos, or better yet find someone who'll coach you a little on casting. Take lessons if you can afford it.
Finally, don't worry too much about being an instant casting pro. You're going to get tangled up, create wind knots, and loose some flies. You may snag yourself occasionally so wear a hat and sunglasses.
I really want to stress not worrying too much about how you look to other anglers, just keep fishing and it'll come.
Remember, it's about having fun!

I started with a $10 investment. Bought a fly rod and reel filled with line at a flea market. Made a few flies and started catching fish. Later I added a few store bought flies but enjoyed making them myself. I still have that rod and can catch trout just about as well as with a $500 rig. Check craigslist or ebay too if your budget is limited. I learned a long time ago that expensive rigs are for show. If you put the fly where it is supposed to be and the fish are there, it catches fish.

Wanna learn the right way?,.... do not just buy a rod at WalMart strictly because it is the lowest price rod you could find. What you need is a knowledgeable angler, or salesman to go with you, or tell you WHAT ACTION the rod is that you picked up! If it is a fast action rod, OR, if it is a slooooow action, very whippy rod that you picked up, you will be severely handicapped trying to learn how to cast the rod. Trust me. Get a med. to med/fast action rod that has been correctly determined to be of that action. I have some inexpensive rods that I often use today, that are of the med./fast action, and perform great. They do not have to be upgraded if you do not want to upgrade them down the rod. They cast, and fish great.

If you don't have a fly fishing buddy to help you, patronize your local fly shop, preferably one with a wide selection AND price range of fly rods, reels, fly line, flies, etc. They can tell you about the best fly fishable waters better than anyone. Tell them your budget (use what you learned above) and they should be able to set you up.