How do you check if injector is firing or not?

There are several ways. Most people use what is called a noid light. To use a noid light you unplug a fuel injector and plug a noid light in to the harness. You turn the engine over. If the noid light flashes then you have injector pulse. Another way to check is to use a low wattage test light. Unplug a fuel injector, and plug one end of the test light to each wire from the harness. Crank the engine over and see if the light flashes.