To begin fly fishing there are a few essentials you will need.
You must have Polaroid sunglasses to see the fish. You can start with some inexpensive ones or spend more and get a pair that you will use in everyday use as well. Fly Shops carry a big selection as well as sunglass stores just be sure they are Polaroid. They range from $15 to $300.
You must have waterproof rain gear, jacket and pants, or if you have waders just a jacket. I learned this on my first float on the Madison River in Montana. When the day started it was 80 degrees, sunny and lovely. I had a Nike shell that was water resistant. By 2 we had pulled off the river and were huddled under a cottonwood tree being hailed upon. Luckily the guide had an extra jacket for me. By pink drink time, around 5, it was 80 degrees and lovely again. You know what they say about the weather in Montana, if you don't like it, give it an hour and it will change.
A pair of waders and wading boots are a good investment. I was lucky that Shelley had extra gear to get me started. Again I would say start with entry level and upgrade once you are hooked. The less expensive waders are not as breathable or comfortable but will do the job and keep you dry. After 2 years of fly fishing Dennis and I were up in Tahoe, California and the fly shop let us try the more expensive breathable waders for a day. At the end of that day we were sold and bought them. It all depends on your budget. Fly shops and manufacturer's web sites will have lots of information for you. Check out our links.
If you are taking classes or going to a school they will most likely have rods and reels for you which is great because this can get really expensive. You want to see how much time you are going to be spending fishing before you put out the money. If you get hooked on fly fishing the gear is never ending, always a newer, better, lighter, faster rod and of course more expensive, so put off the obsession as long as you can. If you are just starting let the fly shop know that you are a beginner. You may want entry level equipment and upgrade later. Trying out different brands and weight of rods, at a class or with a guide, can be really useful before purchasing.
Get your gear and get out there and fish!