There is no real easy way to tell if an injector has gone bad. Effects of a faulty fuel injector would be an engine misfire or rough running. If the vehicle is Throttle body injected it may be as easy as removing the air cleaner and checking for fuel spraying out. I should also point out that an injector does not have to stop working (no clicking) for it to be bad. An injector that flows too little or too much fuel is also considered bad. The method I use to determine the state of a fuel injector is by whats called balance testing. This involves hooking up a fuel pressure gauge to the vehicle priming the fuel system and "firing" the injector by means of a special tool designed for this. As the injector is firing I watch the fuel pressure gauge to see how much pressure was lost during firing. The test is repeated on all remaining injectors and the amount of pressure lost (pressure drop) during teating is averaged out. All injector drop readings are compared to the average, if there is a difference greater than 2 psi it determines an out of spec injector. Obviously if an injector does not drop at all it automatically needs to be replaced. Also if an injector drops too little (lean) it most like can be cleaned and not replaced, but any injector that is too rich (drops too much) has to be replaced.