If the car is less than 48 months old, the best way is to let the dealer fix
it under warranty.  Out of warranty DIY, get out your DMM (digital multi
meter) and test the battery voltage with car on and also off.  With the car
on (engine running) you should get around 13.5-13.7v at the battery.  Less
than this usually indicates a bad alternator.  A good reading with the car
running and a low one (12.5v or less) with the car off usually indicates a
dead battery.

Kyle.
98 740iL
97 M3