The hoops should be the same for any NFA item.
1. Purchase the thing you want.
2. If applicable, wait for it to ship to your local dealer.
3. 99.99% dealers will help you out with the paperwork. Fill out your form 4 in duplicate, and there's another form I forget the number of. And you need 2 FBI fingerprint cards, that I forget the number of. Your Class 2/3/72/whatever dealer will know (if not, you probably shouldn't buy from them).
4. If filing as an individual, have your county sheriff, chief of police, or whatever the highest ranking police officer in your county is, sign both copies of the Form 4. If the sheriff won't sign, write the BATF and ask for a list of individuals whose signatures they would accept, and ask them one by one. Your local dealer also may have ideas.
5. Get your fingerprints taken, and printed out in duplicate on the cards. Once again, your local dealer should be able to tell you where's the best. In PA, the state police will do it free of charge.
6. Get 2 passport-sized color photos taken.
7. Affix the photos to both copies of the Form 4. Some people are superstitious about this part. I used Scotch tape.
8. Mail both copies of the Form 4, both copies of the other form, both fingerprint cards, and a check or money order for $5 (AOW only) or $200 (everything else), to the ATF. Mine was a personal check payable to "Bureau of Alcohol, Tobacco, Firearms, and Explosives," which just barely fit on the payee line. Everyone has their own idea of what to write on there to make it go through faster, but that's what worked for me.
9. The hardest part. Wait.
10. Notification will be sent to your dealer, not to you, so you'll need to wait for them to call/e-mail/whatever.
10a. If your application is turned down and you don't want to try again, you are legally allowed to sell the NFA item. It's your property since you paid for it, but you cannot legally possess your own property until it's registered to you. So in other words, it doesn't belong to your dealer, and your transactions with him to resell the thing should be from that perspective. I'd say it is reasonable to still pay the transfer fee even though it didn't go through, though. The dealer still did the same amount of work.
11. Take possession!
12. It's a felony for anyone to possess a Title II item which is not registered to them, and being in the same room as a Title II item while the owner is not at least somewhat present, constitutes possession. If you live with anyone else, you'll need a safe if you don't already have one, which only you have the key/combination to.
