I'm no expert on the topic, but I'm probably a few weeks/months ahead of you in the process. First step is to find a suppressor you like/find a class 3 FFL who can point you in the right direction.
I found this suppressor for .22lr that seems to be a VERY popular suppressor
Step 2 - decide what gun you want to mount it to. The Walther p-22 comes with a threaded barrel - you just need an adapter to extend the barrel beyond the slide - most places that sell suppressors will also sell these ($15-ish)
-- step 2 can wait - come to think of it you should go straight to step 3 and come back to step 2
Step 3 - go to the class 3 FFL and buy your suppressor - you have to fill out the paperwork, do fingerprints, but they won't actually charge you for it yet. They have to have the actual suppressor's serial number for your paperwork ($200 tax)
You also have to talk to the sheriff in the county in which you reside and get his approval - not a problem in many areas - can be a problem in some.
Send in your paperwork - and the wait begins. So does the second guessing - I.e. should I have gotten the suppressor for the AR-15 instead of the p-22? Because If I had bought the other one, it will still work for the p-22, but I won't be able to use the sights because the diameter is too big.
After 6-8 months, your paperwork will be processed, and you'll be able to pick up (and pay for) your suppressor.
Now that you've got the suppressor bug, and have been through the process once, you'll now start buying suppressors for all of your guns - costing you $500-700 more per firearm than you were spending. But you'll have a lot of fun and preserve your hearing.
Just a prediction if you're anything like me - and since you're on this forum and looking at this - you probably are...
Hope it helps - FYI there's a really good FAQ section of the gem-tech web site
That will probably explain things a little better than I have.