It's a pretty easy install... although expect to spend about 2 - 3 hours if this is your first time doing something like this. I just installed a single din in my 2005 corolla this past weekend and short of losing a couple of screws, everything went smoothly. You will need to buy a single din dash kit for your corolla. I suggest the Metra kit. You can do a search on ebay. It is well built and will hold your stereo securely and fits well into the Corolla dash. You will also need to buy stereo wiring harness... again on ebay. For install instructions, check out this link:
http://www.net4free.org/Other/nshahzad/stereo.html. The author says you need an allen wrench to remove the stereo but on my Corolla, I needed to use a socket wrench. I suggest you disconnect the negative battery terminal before doing this as you don't want to risk short circuiting anything. One thing missing from the instructions is that you will need to shift the gear shift to low gear if you want to swing the climate control panel aside. Of course if you disconnected the negative battery terminal, you wont be able to do this. You will have to pop open the shift lock to be able to shift without power. The installation will take some time, but it will be worth it. The sound from the speakers will also improve with the aftermarket head unit. Be careful not to lose any screws as I did. I dropped a couple in the compartment where the shifter is. Make sure then when re-attaching the panel with the air vents back onto the dash that no wires are blocking the vents.