The "click" you hear when jumping the wires is the clutch kicking in. (or should be) The pulley on the compressor is always spinning when the car is running. The clutch is an electromagnetic thing and when it clicks it will "lock up" the compressor to the pulley and it runs. If your system is dead IE no pressure then it will be spinning but there will be almost no load so it may seem that the compressor is not running. You should be able to see if it's working because when the clutch is resting the inside will not spin, when engaged the inside will spin and it will be obvious when you see it.
However it has been said here many times that A/C work can be VERY DANGEROUS if you don't know exactly what you are doing. At the very least you should read the Hayes manual that deals with nothing but A/C systems before doing anything.