What are you referring to Todd?
Are you wanting just to own some Class III stuff, or are you wanting to become an FFL dealer that can deal in Class III?
If you are just wanting to OWN some of this stuff, you don't need to get a "Class III" License. THIS is if you live in one of the 35 C-3 friendly states. There is an AWFUL lot of information, and unfortuantely, misinformation out there. BigMike gave you an excellent resource if you are looking to become a dealer. However, just for owndership, you file one of two types of forms. A Form 1, or a Form 4, Depending on what you want to do.
Form 1's are only good if you want to actually MAKE your NFA item. Such as a Short Barreled Rifle, Short Barreled Shotgun, Any Other Weapon, Suppressor, or in SOME areas, Destructive Device. These ALL STILL have the $200 federal tax.
Form 4's are for a Tax Paid Transfer to you from a dealer. Essentially it's the same process as a Form 1. 2 passport photo's, 2 complete FBI type fingerprint cards, $200 check, and a Chief Law Enforcement Officer putting his/her signature on it.
I could type several pages on this and still have more to go. That's the very basic stuff. Tell us what you are wanting to do, and we can be of more help
Here are a couple helpful links.
(downloadable ATF forms)
Hope this helps!