To remove the factory head-unit (providing it's in the factory location), just take off the plastic surround in your Corolla by unscrewing the two bottom screws, pulling off the air-con buttons and unplugging the plugs from the back. In order to unplug the plugs, you must slide the console piece out slightly so that you can get your hand behind there. The plugs will be directly below each other. Once disconnected, the console piece will slide out straight towards you.
As for the installation of the aftermarket head-unit, it is a lot easier if you buy a harness. Then it will simply be a case of plug-and-play.
Like this:
http://www.carxtc.com/servlet/the-14...1997%2C/Detail
Then you just unscrew the stock head-unit from the mounting brackets and unplug the power and antenna plugs at the back. Once you've done that then you slide your aftermarket head-unit through the hole in the plastic surround, plug in the aftermarket harness (if you decide not to get one then just splice the wires and follow the instructions that came with your head-unit), plug the radio antenna back in and then re-install the plastic surround. Finally, put the face plate on and then you're done.