I've had to type these same basic instructions for different people across several different forums in the past few days, so figured maybe it should be shared here too. This is what to do if you're having car battery/alternator issues:
Make sure the belt is properly tensioned and not slipping. Battery at rest should be 12.7V when charged. If not, charge it up separately. Make sure battery is clean*; terminals, connectors, and cables un-corroded and tight; and main grounds uncorroded and tight.
When you start the car, the battery voltage should jump to between 13.6-14.7v with a good alternator and no other loads. Then turn on headlights. Voltage shouldn't drop much - at least not below 13.6v. If all that tests good, with the engine running, pull the positive cable off the battery. If the car dies, that points to the alternator. See if any of your local parts stores have a roll-around test cart to confirm it's bad.
If you do order a new alternator, try to do so from a parts store that has a tester, and have them test it straight out of the box. A lot of alternators are poorly rebuilt ones these days. I once had 6 alternators in a row arrive bad out of the box.
*battery acid on the case of the battery will conduct electricity and be a parasitic draw. Take a voltmeter and place the leads on random locations on a dirty battery. If it reads a voltage, that's current flowing with resistance through the gunk.