Find the suppressor you want. Pay for it. The dealer should fill out the form right there on the computer for you, and hand it to you, minus the stuff you have to do yourself.
Get a passport photo taken, to affix to the form.
Take the form to a chief LEO, such as Chief of Police, county Sheriff, or DA. I believe a few others may be able to sign off as well - not too sure. You may want to find out for certain if a local CLEO is willing to sign off in the first place, before you even put money down at the shop.
Get your fingerprint card completed. I did this at the county jail. They may or may not charge you a small fee, like $5 or so.
Send all this to the ATF address printed on your form 4, along with a cashier's or personal check for $200. Wait far, far too long for the dealer to recieve it back. Go to the dealer after he calls you, and walk out with your suppressor.
My wait time from the ATF for my first supressor was 49 days, from the day I mailed the form to the day I picked up the suppressor.
Currently, I am at about the 35 day mark on the next one. Some people have had to wait as much as 10 months, from what I have heard.