What I did for my 04 Corolla was remove the head unit, cut the speaker wires, and ran four pairs of speaker wire from the head unit to my amp (two pairs for the both front left and front right speakers).
The four pairs are used to run the signals to your amp and then from your amp back to your front speakers.
I found out the correct color of the wires here:
http://www.installdr.com/Harnesses/Toyota-Wiring.pdf
but you may want to double check that because mine was a corolla and not a JBL system.
It was sort of confusing keeping track of which wire went to which channel and which was pos and neg, but it worked.
For the rear channels I just used the stock wires that went to my rear speakers and ran those to the amp.