Basically, the clicking noise in the solenoid is an indicator of insufficient voltage and or current from the battery.
Your cables and wiring might be corroded. Check and clean/replace as required. Be sure to also check the ground straps which attach from the motor to the negative terminal on the battery and to the frame of the car. Also check the condition of the cable clamps which attach to the battery terminals.
Your battery could be old or discharged. Try replacing the battery with a new one (use the correct size). If this fixes the problem at first, but it comes back after a while, you have a problem with the alternator not charging the battery. This could be due to corroded cables or wiring, or more likely a bad alternator. Alternators eventually wear out their brushes and will not charge the battery sufficiently. Have the alternator checked by a competent repair tech.
Starter solenoid could be defective. Repair or replace.
Starter motor could be defective. Repair or replace.
Hope that helps.
-Prologue