well sorry it took so long... i was pretty busy today... but yeah i got the pics up now.
here is the engine:
as you can see how the thick wire goes to the back of the altenator, a little shorter wire goes to the side of the altenator and the long small wire goes to the ac compressor:
here is a closer shot of the altenator with some lighting on it, so you can better see the wires of the thick ones and the small ones from the long small one that goes to the ac compressor:
I hope this helps out man, and i understand you just got a nice cheap car to commute with, this car is awesome and i have always loved it since i got it... if you need anymore help, just post up and ill try my best to answer them and help. good luck on your corolla man.