If you're not the reading type, go ahead and watch this video where I go through and etch the USB logo necklace that inspired this instructable.
https://youtu.be/ZgVNVejMkH4

Step 1: Prep Your Piece

First off, use acetone to strip all the oil off of your project piece.
Next, you're going to want to cover all of the copper that you don't want eaten away. I got away easy with my piece only needing to be partially submerged.

Step 2: Prepare Solution!

This is probably the easiest part. Create a saturated salt solution.
This is basically just warm water and salt.
Actually, it IS just warm water and salt.
Stir well.

Step 3: Some Assembly Required

Now with your piece prepped and the stencil adhered, you're ready to begin etching. Place your copper in the solution with the positive lead attached to it, and your negative lead(in this case a length of copper clad grounding wire) across from it.
It is imperative that these do not physically touch.
After these have been prepped, go ahead and hook them up to your power source. I used a 6v Lantern battery, but this is something you can choose yourself as different power sources will result in different quality etches.

Step 4: Waiting

Given that you're etching is happening on the microscopic scale, it'll take a little while. you can check on it every 20 minutes to half hour, but I let mine go for a full 70 minutes before I deemed it acceptable.
Go ahead and do something to pass the time.

Step 5: Cookies Are Done!

Now that you've given your piece ample time to etch, go ahead and remove it from the power source and then from the solution.
Beware that if you're not careful, you can make a royal mess.
Rinse your piece under water to remove and residual gunk and then peel away your resistive material.
You should now have the design etched into your copper.
The depth may vary depending on distance between electrodes, Wattage, salt content of the solution and the amount of time you waited, but so long as you didn't rush the process it should be acceptable.
Go ahead and sand it with emery cloth or steel wool to bring out the shine.