what kind of paperwork goes in to getting one of those?
Read this to make sure your state allows ownership.
http://www.advanced-armament.com/owners.asp
There is another thread do a search on silencer, it has 4 pages of info.
In order to get one you must purchase your suppressor from Earl for example.
You will have to fax him your driver's license and the Class III license from your state Class III dealer. You can find a list of dealers from gunbroker.com. Some dealers have Class III licenses but don't do dealer to dealer transfers ($75-$200).
Once Earl has the paperwork, he files it on his end (2 weeks).
Then he sends the suppressor to your dealer (2 days).
Your dealer will have you get the FBI fingerprinting cards and applicable state cards which you submit to your state police CLEO(Chief Law Enforcement Officer) for approval and signature (2-3 weeks).
You will receive the paperwork from CLEO signed off on the ATF forms.
Have your dealer submit all the forms to ATF with a $200 money order for the transfer stamp from ATF (4-6 weeks).
Goto your dealer to sign and pickup your can.