Tying your own flies can be very rewarding and relaxing. It also has another benefit in giving you something to do if you are unfortunate to live where the rivers are frozen in winter, or fly fishing is closed for some months each year.
The tools are simple. You could make most of them yourself, however it would be best for beginners to buy at least a fly tying vice. There have been over the years quite a number of different vice types manufacturered. In my opinion, the cam type of vice is the easiest to use. This is a vice that has a cam lever to open and close the jaws. It's adjustable to various angles and hook sizes. Quick and easy to open and close.
The next thing to get your hands on are some hackle pliers. These are also a cheap spend, but really worthwhile. They are a little difficult to make a pair yourself.
Apart from these items, you'll need a pair of curved scissors with sharp points and another set with small straight blades. You probably could also do with a needle that is pushed into a stick. This is for fixing hakkles that have been inadvertantly wound under. You can also use it for putting laquer onto the finished head.
What sort of hooks should you use? My advice is to not fall for the trap of using any old hook. Buy proper fly hooks. These have a tapered shank and are usually hollow ground. These are lighter than normal hooks, a real advantage in dry flies.
The tapered shank lets the head, especially the eye of the fly be tied tighter and smaller. When you consider the work involved in tying a fly, why waste effort on the wrong hook. If you make a mistake, all you need to do is cut the fly off the hook and start again.
Something you could consider these days is the opportunity of actually buying a complete fly tying set. These sets cost only around $50 or so. They have vices, scissors, pliers, hooks and all the feathers and fur you need to get started. Some even come with videos or DVD's.
Whichever way you go, it is a cheap way to spend many an hour, in preparation of catching your next bag of fish. The satisfaction of catching your next trout on a fly you tied yourself is immeasurable.