This is a topic that gets asked quite often. Maybe someone with better search skills can find one of the threads and post it.
A lathe.
Second, assuming you are going to buy all your blanks and don't intend to resaw them, you need a way to cut the blanks in half. You will find that the Grizzly is a popular bandsaw on this forum. You could get by with a small miter box.
Next, you need a way to drill the blanks. That involves either a drill press with as close to 3" of travel as you can afford or some people drill on the lathe. You will also need about a Gazillion drill bits.
Glue, sandpaper, Multi-Mesh
A way to trim the barrels. Either a disk sander, a barrel trimmer and/or one of the new ones from Firefyter-emt.
Bushings, kits
Turning tools. Some will say, get the best you can afford. Crown Pro-PM are good. Others use cheap ones from Harbor Freight and just sharpen more often.
Some way to sharpen your tools. Slow speed 8" grinder, slipstones, strops, Tormek, Jet wet grinders. Again, according to what your pocketbook can afford. If you buy the best first, you'll probably save money in the long run. You'll probably end up buying them eventually anyway.
Some way to keep the dust out of your lungs. A very good dust collector (cyclone style) would be preferred. I use a half respirator with cartridges. I think masks are a waste of time, that's purely my opinion though. A lot of people like the Triton respirator. Mine is only powered by my lungs.
That's what I have for starters. BB at Arizona Silhouette has some books for sale that would show you how to get started. He also has a video which is where I really got started. Get his and Ed Davidsons (YoYoSpin's) video together and you'll be well set up.