Before you go after the starter, you need to check the battery and terminal connections. Here is a simple test:

Turn on your interior lights. Look at the lights and attempt to start the engine. If the lights go really dim, then it's more than likely a bad terminal connection at the battery or a bad battery.

The clicking sound is the starter solenoid. What happens is that the solenoid gets enough juice to close its contacts making a click. But as soon as the starter begins taking its huge amount of current to turn over the engine, there is a large voltage drop (due to bad battery or battery terminal connection). When the voltage drops, there is not sufficient current to hold the contacts shut so the spring opens the contact in solenoid. But, wait, as soon as this happens there is plenty of juice to hold the solenoid closed and process begins again. Hence the clicking noise.

Check the battery and its terminal connections before you go after the starter. The dimming interior lights is a tell tale sign that there is not sufficient juice to turn engine over.