You can check the charging system with a voltmeter, but it may or may not tell you the true state of the charging system. In general, alternators should put out about 14+ volts when they are charging correctly, but this will not tell you what the alternator will do under load. To do that, you would need to have the voltmeter connected while driving. If the voltage drops under load, the alternator is probably bad. (I'm assuming you have an alternator that has a built-in regulator.)
That's why technicians use ammeters to check charging systems. Some local auto parts stores have this capability. You might check with NAPA or another local vendor. They'll be happy to sell you a new alternator if the old one is defective.
