Skeeter, I'm sorry I didn't see your post sooner. I just recently started looking at the "workbench page".
Most of us start with brass tubing to make the ferrules. You can buy brass tubing, aluminum tubing and other metal tubing at onlinemetals.com or other online suppliers. Brass and aluminum can be worked on woodturning lathes. Once you've decided on what size you want, and have it in hand, mount it in a 4 jaw chuck and use a thin parting tool to cut it to your desired length. I use a cartridge case chamfering tool to chamfer the cuts on the inside and outside of the tubing.
Several trumpet yelper makers use cartridge cases as ferrules. Steve Lumma makes some really nice ferrules, but until you have your final design figured out, tubing and cartridge cases will work just fine. Both are traditional ferrules.
Other than the standard turning tools of a chuck, spindle gouge, parting tool, roughing gouge, and maybe a skew, a couple other accessories can come in handy. Some guys use a tapered reamer to flare the inside of the bell. If you're going to turn the inside of the bell to flare it, you'll need a spindle steady.
The biggest challenges with a trumpet yelper are knowing how to hold the work on the lathe, and drilling the holes. You can drill the holes on the lathe or in a drill press.
Sometimes the blank is held between centers, and at other stages the blank is held with either a 4-jaw chuck or a collet chuck.
Mouthpieces can be made from bone, usually camel or giraffe leg bone, from acrylic, buffalo horn or gemsbok horn. I would not suggest starting with gemsbok horn. One horn will cost almost as much as small piece of ivory and knowing how to cut it is a little tricky, and you'll only get one mouthpiece from one horn. Delrin is a big favorite for those just getting started and its cheap and easy to turn. Then there's also ivory.
How you hold to the blank, how you do the drilling and turning in the beginning, mostly depends on what tools you have on hand and how much you're willing to invest in some other tools.
Hope this helps you get started.
Danny