Measure the voltage at the battery with the engine running at about 1500 RPM. If over about 14 volts, your alternator is good. If not, then suspect the alternator. If you have the time, charge the battery and let is sit for 24 hrs. If not at 12.6 vdc after that time, your battery can't hold a charge. You don't want to shotgun parts replacement - it can get expensive if your shotgun is off target.