Here is everything that I used: Orbital Buffer (with Polishing Cutting Compound), Hair Dryer, Putty Knife, Goof Off, Simple Green Cleaning Spray, Paper Towels and a Micro-Fiber Rag.
Example of the side "Toyota Tacoma" badge removal:
Step 1.) Apply "hot" air with the hair dryer for a few seconds and then slowly and carefully slip the corner of the Putty Knife blade underneath a corner of the badge and gently (as you're blowing heat on the upcoming letters) move the Putty Knife along, lifting the badge off one letter at a time. You won't peel all of the adhesive underneath, but that's okay...
It should look like this once you peel the badge off:
Step 2.) Use the Hair Dryer again to heat up the adhesive and slowly "rub" or "pick" the adhesive off -- when you get it starting to peel it will roll, and by doing that the adhesive will gather more adhesive. Heat ahead of where you're picking at, it will help the upcoming adhesive come off easier -- if you're like me I have no fingernails so this was a pain in the a$$ step.
It will now look like so:
Step 3.) Once you have all the major adhesive off, hit it with some Simply Green Cleaning Spray and wipe all that gathered dirt off.
Step 4.) Use a folded up paper towel with some Goof Off on it to get some of the dirty adhesive completely off of the paint, repeat this a couple of times - each time switching to a new part of clean paper towel.
After Step #4 it will look like this:
Step 5.) Use the Orbital Sander (I found it best on the highest speed for 20-30 seconds moving it all around the area) -- you can also use whatever Polishing Pad you have, it will just be more work --> either way use the Polishing Cutting Compound you will ultimately come to this result:
Repeat Step #5 as many times as desired --> I had found it takes 3-4 times to become completely satisfied with the end result.
I know it's not easy to see, but the paint was very clean & reflective at this point but believe me, if you stand back you can't even notice there was a bright chrome badge there before.