Hi,
get a multi meter and take the voltage reading across your battery terminals with the car running. You should get about 13 to 13 and a half volts, if so your alternator is producing the correct voltage for your battery. If you are getting excessively high voltage above this it can "boil" your battery and when you switch on all your electrical systems (lights, radio, etc) the voltage should not drop below 12 volts. This is a good place to start with your diagnostics.
Cheers now
Ken Chapman, May 2007