Get in touch with a Class 3 dealer. They fill out their part of the paperwork and then mail it to you to finish and submit to the ATF.
You also need to decide what suppressor you are going to get first, since all that info needs to be on the Form 4.
The process goes as follows:
Decide what suppressor you want.
Get in touch with Dealer, send them money, wait for them to get the suppressor in their possession.
Dealer fills out his parts of the paperwork.
Dealer mails you the Form 4' fingerprint cards, etc.
Get fingerprinted, photos, and CLEO signoff. (I won't touch the trust method with a 10' pole, neither will my dealer and many other people. CLEO signoff is not a problem for me, but for others it may be their only option.)
Mail in all the paperwork with a $200 check.
Wait for ATF to approve the Form 4 and send it back to your Dealer.
Take possession of NFA item from your dealer.
I don't carry a gun to go looking for trouble, I carry a gun in case trouble finds me.