There is no federal license or permit required to own a silencer in the USA unless you live in a state that prohibits civilian possession but makes an exception for those that are licensed to manufacture, deal or import them as a business.
Anyone who can legally own a gun can own a silencer in the 38 states that allow them. The paperwork is a simple routine matter (with one exception) and the ATF never denies authorization to possess a silencer as long as the forms are filled out correctly. An individual is required to obtain their local sheriff’s signature on the tax stamp application; some refuse to sign. Using a Corp or trust to own the silencer is a way around this.
I agree with everything JohnKSa said, but there are exceptions to the "anything that reduces noise is a silencer". The long extension tubes made for shotguns that reduce noise are not classified as silencers by the ATF. http://www.metrogun.com/
The ATF also says that non-portable devices that are not attached to the gun but are intended to reduce noise are also not silencers.
There are no portable silencers that are capable of completely silencing a firearm. A silencer only reduces (but not completely eliminates) muzzle noise and does nothing for action, bullet noise or impact noise.
The feds use two legal terms for gun noise reduction devices. Those terms are silencer and muffler. Telling a police officer that your device is an unregistered muffler is a confession to a crime that can result in a minimum of ten years/$10,000.
Good silencers are easy to make on a lathe with a minimum of experience. In my opinion they are the nicest accessory a person can add to most guns. Once I shot suppressed I did not want to go back.