Same state as Zak said. If you haven't gone through the process before, it's easier than you think. The absolute easiest method is to use a Silencershop Kiosk if you can find a local dealer who has one and if Silencershop has what you want. Otherwise any store that has suppressors will help you with the paperwork but you'll often get dinged with a hefty transfer fee through your dealer if you order a suppressor online outside the Silencershop.
My recommendation is to figure out what you want and then if Silencershop doesn't have it, use the Silencershop dealer locator to figure out who the dealers are in your area that do NFA items and start calling around trying to figure out who has what you want in stock. I'm admittedly a TBAC fanboy and I've done this with both of my suppressors because it's always hard to find the popular TBAC suppressors in stock(but thankfully I live 15 minutes from one of their biggest dealers). Its a little work but often enough someone somewhere has what you want.
As to the paperwork if you can pass a normal 4473 background check you can get a suppressor. There are a few more places to sign and whatnot, and you'll have to submit photos and fingerprints but your dealer can help you with that and it usually takes no more than an hour. The hardest part really is figuring out what you want because there are a ton of really great suppressors on the market at the moment.