Generally, a constant clicking noise and no crank situation is a sign of not enough power to the starter. What happens is that when you turn the key on, you can hear the solenoid close. If there isn't enough power, the engine won't turn over and the starter will act like a dead short, drawing down the battery voltage. Once the voltage is low enough, the solenoid will not have sufficient power and it will open allowing the voltage to come back up. This repeats at a fairly rapid rate causing a clicking noise. If this is your problem, you probably aren't getting enough current to the starter because of bad batteries or bad connections although it still can be your starter.
If you only hear one click, that is your solenoid closing but for some reason, power isn't going to the starter. It could be an internal problem in the starter or it could be a bad connection leading to the starter.
I would start by checking resistance with a multimeter on your leads and also check battery voltage. If all of that checks out, I would pull the starter and have it bench tested at your local autoparts store.