It must be legal in your state to do so, most states allow NFA
There are two ways you can purchase NFA items
#1 As an individual. If purchasing as an individual your Chief Law Enforcement Officer must be willing to sign off on your forms. Some will some won't
#2 Purchase through a trust, LLC, etc. Basically if your CLEO won't sign off this is your only option
Go to a class 3 dealer in your city/state. They will know if a CLEO will sign off or not. Some people (including me) prefer to purchase through a trust. The benefit being that the trust owns the item, and anyone that you name on the trust is allowed to use the NFA item. If purchased as an individual you must maintain sole possession of the NFA item and although someone else can use it, it must be used while in your possession.
Pay up front for the silencer, the dealer will fill out an ATF Form 4. You send two copies of the Form 4 along $200 per NFA item (this is a one time fee, per NFA item) with the appropriate paperwork depending on how you bought silencer (trust vs individual). The dealer maintains possession of the silencer until you are cleared/approved by the ATF. ATF sends the approved form back to the dealer you bought the NFA item from. Dealer calls you, you go to dealer fill out ATF form 4473, take the NFA item home.
Listing of states that allow NFA items along with some more detailed information
http://www.silencerco.com/?section=Education&page=Ownership