How do I get the original radio out of my 07 Corolla?
Leave the door unlocked, and the window open for a couple of hours in Brooklyn, and that should take care of it for you. 
Chances are you need to remove the surrounding trim pieces, and then unbolt the mounting bolts, and then disconnect the wiring and antennae, and it should slide right out.
BC.
Google Toyota Corolla radio removal. I just did and it looks like instructions for an 06 is the top choice.
-golfclap-
Well played.
Often on factory radios there’s an annoying little screw holding it in that you have to get behind the radio to access. Depending on the arrangement of your dash, you might be able to get to it by diving underneath, but you might have to start taking pieces off.