When there is a problem starting or driving a vehicle, two of the most important checks involve the ignition and the fuel systems. The questions most mechanics attempt to answer first, "is there spark?'' and "is there fuel?'' will often lead to solving most basic problems. If the ignition system checks out (there is spark), then you must determine if the fuel system is operating properly (is there fuel?).
I cannot list all the specifics about troubleshooting a no start problem here. You should invest in a repair manual, just make sure it includes all the troubleshooting information.
If I remember correctly, your corolla should have a distributor. Usually when there is no spark, you shoud check to make sure your cap and rotor or ignition coil do not need to be replaced. The distributor cap distributes the electricity from the ignition coil to all spark plug wires. The distributor cap is usually made of a hard plastic with internal copper contacts. The cap takes a lot of abuse from high electrical voltages and should be inspected and or replaced during a regular scheduled tune up.