Most of the forms can be downloaded at
www.titleii.com - I don't think they have the fingerprint cards, but those need to be on heavy cardstock with the proper routing numbers for the firarms & explosives division.
Assuming suppressors are legal to on in your state, here's the proceedure in a nutshell:
Find a class 3 dealer in your home state. Pick out the suppressor you want, or have him order it from the manufacturer. Once he has the can you want, you will fill out a BATFE form 4 (in duplicate), along with one copy of the US citizenship certification, two FBI fingerprint cards, and a check for the transfer tax of $200. You'll also need two passport sized photos for the two F4's. The F4 will needs to be approved by your local chief of police, the sheriff, or any one of a few other officials that qualify as a CLEO (Cheif Law Enforcement Officer) with jurisdiction over the place of your residence. Theres a complete list of qualified officials on the instruction side of the F4. Be aware, the local CLEO can decline to give you a "sign-off" for almost any reason, or for no reason at all, so be polite and dress appropriately (leave the "uni-bonger" T-shirt at home and don't go in looking like you just rolled out of the local bar.)
On the reverse of the F4 you'll notice a section asking why you need the NFA weapon in question. Generally good and acceptable answers are "for investment and collection", "for all legal and lawful purposes". "Because the voices in my head told me to" is not. "Self-defense" is not.
Once you have it all together mail everything to the address on the front side of the form 4 and wait about 3-4 months. Your dealer will receive the approved form and let you know when you can come pick it up and take it home. You cannot take possesion before he has an approved copy in his hands. Your dealer will give you the original copy of the F4 (BATFE keps the other) - keep it somewhere safe and make copies for keeping with the suppressor.