The Secret Friend Method
Go to the estate of one of your secret friends while he's there and walk down to his dock. When you're on the dock, perform the fishing glitch, which will take you to a neighboring dock. During the glitch, click the "X" and ask your secret friend to leave his estate. Once he has, scratch a doodle and head over to a Cog HQ in a different district. When you're inside the VP/CFO lobby, whisper to your friend (must be in a separate district) to constantly whisper to you. Leave and re-enter the lobby but as you reach the doors, click "Whisper" and then "Go To." Once the inside of the lobby loads again, the district message should pop up. Click "Yes" and you'll be teleported, wearing the cog suit, to the other district. Using this method, only you will be able to see the suit on your avatar.
The Fishing Glitch
Leap from a dock proper and cause your character to land on a neighboring dock's extreme front edge. This is successful when your character begins the fishing animation, but looks to be still walking forward; that said, this glitch is rarely successful.
Cog HQ Method
Begin in the VP/CFO lobby in a Cog HQ and enter the elevator there. When the Cog VP or Mata Hairy begins to utter their first phrase to you, quickly hit "ALT-F4" to log off. When you log back on, you will be in your estate wearing your cog suit.
Effects
When you successfully perform the secret friend method, you will be able to use cog phrases that others will be able to see. Also, you'll be able to see your cog suit while others cannot, so it will seem to them that you are only using cog phrases as a normal Toon.
When you successfully perform the Cog HQ method, you won't be able to use any cog phrases nor will you be able to see your cog suit. Rather, you'll appear to all the other Toons to be wearing a cog suit in your home.