First make sure it's legal for you to own in your state. Second you need to find a C3 dealer to handle the transfer (in your state). Find the suppressor (some dealers may have some in stock).
Usually you pay 100% for the suppressor up front, then fill out a form 4 (with CLEO sig, picture, fingerprints) and the citizenship form and send $200 to the ATF.
www.titleii.comThen you wait and wait and wait some more. After that you wait some more and then you finally get the nice little stamp and you get to take it home.