If the car's starter clicks and the engine does not turn over, this could be caused by several things. The most common cause of clicking when the car is being started is a low battery. Most people would assume that the starter is bad if it only clicks, but low-voltage can cause the starter to make this sound.
The battery is the heart of the starting and electrical system. If the battery has been drained or has a weak cell, this can cause the starter to only click. Many times the battery could just be drained due to a door left slightly open, making the dome light stay on. Other times a vanity light or a phone charger could be left on. During my time as a master auto technician, I've had a trustworthy co-worker close me up in the trunk so I could make sure the trunk light went off when the trunk was closed!
In order to test the battery it must have a good charge. If the battery is not charged completely the tester will indicate that it needs to be charged before testing can proceed. The first step when checking the starter and electrical system is to make sure the battery is in good condition. Most parts stores will check batteries for free. Once it's determined the battery is good the rest of the system can then be checked. Loose or corroded connections can also cause a clicking and for the car not to start.
Starter
The starter solenoid on many Ford vehicle's is on the inner fender well, on most other vehicles the starter solenoid will be mounted on the starter. The clicking that is heard many times is the solenoid. But low-voltage either from a drained battery, bad battery or poor connections can cause this. Most of the time if the vehicle can be jump-started the starter is okay. This would also indicate that the connections to the starter are good.
Alternator
Once the vehicle is running the alternator output can be checked. If the alternator is not charging the battery, it will be drained during the process of starting the car and driving. When the alternator is checked, the voltage and amperage output can be measured. Also the diode pattern will be checked to make sure the alternator will not drain the battery when the engine is turned off. In the past do-it-yourselfers could disconnect the battery while the vehicle is running to check the alternator, if the car kept running the alternator was good. Doing this on computerized vehicles can be harmful. If the battery is disconnected while a computerized vehicle is running the alternator output it can increase sharply allowing excess voltage to spike the computer.
Battery
When purchasing a replacement battery the cold cranking amps required for the vehicle should be checked. It's best to purchase a battery with more cold cranking amps than the minimum required. Also when purchasing a battery you should consider if you want maintenance free or not. If the battery is hard to access or has a cover then a maintenance free battery is preferred. For instance on some Chrysler Sebrings and Chevrolet Corvettes the battery is located behind an inner fender and on a Chevrolet SSR. the battery is located underneath the bed where the spare tire would normally go. If installing the battery yourself be sure to notice which side is positive and negative in case you were sold the incorrect battery.
Terminals
The terminals should be free of damage and should tighten up well. Sometimes especially on import vehicles the battery terminals will be very thin and can have hairline cracks causing a poor connection. Avoid forcing the battery terminals on by tapping them. The battery casing can be damaged causing a leak, if the battery acid seeps out it can cause fast corrosion. If the battery terminal bolts will not tighten, then replacing the terminals is recommended. When the connections are tight you should not be able to twist them by hand.