Suppressors are not legal in all states, but if they are the process is basically the same:
1. Find FFL/SOT dealer in your state (a "class 3 dealer")
2. If buying an NFA weapon like a suppressor from an individual or dealer in another state, it will first have to be transfered to your dealer.
3. Once you dealer has it in his possession, you fill out a BATFE form 4 (in duplicate) and get a signoff from the CLEO (Chief Law Enforcement Officer - usually the sheriff or chief of police in the jurisdiction of your residence).
4. Get two FBI fingerprint cards from the dealer and get fingerprinted when you go in to your CLEO for the signoff.
5. Complete a BATFE US citizenship certification form.
6. Make out a check for $200 for the transfer tax.
Send the $200 check, the two fingerprint cards, the two copies of the form 4, and the US citizenship form all to BATFE.
7. Wait.
8. Wait some more.
9. About 2-3 months later your dealer will receive ONE copy of the form 4 back from BATFE with a $200 stamp affixed. You can now take the suppressor home - its yours.
10. Place your copy of the original stamped form 4 is a very safe place (like a safe deposit box) and make copies of the form to keep with the suppressor at all times.
Theres a lot of good manufacturers - I'd recommend starting with
www.gem-tech.com