Jumper the car and once it's idling properly measure the voltage across the battery terminals. If 13.5 volts or higher - alternator is probably OK but you probably need a new battery (or battery is just run down from some kind of drain -- light left on, etc).
It's also possilbe you may have a bad battery connection (corroided terminals?) or a bad battery to car ground connection. Two other things to check before replacing the battery.