First things first. Check that the battery terminals are clean. Then get the car jump started. Even if the battery is bad the car should run fine. Check that battery with the car running. If you are getting 13-14.5 volts your alt. is good. (really it should be closer to 14) Then take to the battery to any good auto parts store and have it checked. If it's bad, get a new one while your already there.
If the battery is good, then you can get into the possibility of other problems. What your describing is exactly the same symptoms my car had when the alt. died.
