In most cases the problem is with the alternator.
One of the most common issues with batteries not being charged correctly is faulty voltage regulators. The brushes typically wear out which causes the alternator not to charge correctly.
1. Check the fluid level in the battery.
If it is low, add water to bring it to the correct level.
Even if it is a no-maintenance battery you can usually get the vent covers off without damaging them.
2. Charge the battery to a full charge.
3. With the car running, use a voltmeter to check the voltage across the positive and negative post of the battery.
It should read nearly 14 volts.
If not, the alternator may be faulty.
NOTE: Most local parts stores will test your alternator at no charge.
4. Turn off the ignition and check the voltage of the battery.
It should be just above 12 volts.
5. Do not start the car for several hours, preferably overnight, then check the voltage again.
If it is within 1/2 volt of the first reading, the battery is probably good.
NOTE: Most local parts stores will load test your battery at no charge.