Although a clicking sound when trying to start your car may indicate a number of problems, the most common are a dead battery and loose or corroded wiring from the battery to the starter. The corrective steps include testing the battery and connecting the battery directly to the starter assembly.
A multimeter can indicate if a battery has enough charge. If one is not available, or if taking the battery to a local auto parts store isn't an option, trying the windshield wipers or interior dome light can quickly help narrow down the problem. Slow wiper motion, or lights dimming while trying to start the ignition, may indicate a weak battery.
If the battery checks out, visually inspecting the battery terminals and connections may shed light on the problem. Removing the cables and cleaning all the connecting areas often clears up the problem. If the problem persists, testing the voltage across the wires connecting to the starter may expose weak connections or corroded wiring going from the battery to the starter. Bypassing that wiring by connecting the battery directly to the starter can narrow the diagnostic process.