The first thing to do is to check the voltage at the battery, then start the engine and check it again while the engine is running. If the readings are the same - it's a charging problem. You should get a reading somewhere in the mid 14v range while your engine is running. If you do suspect your alternator, double check all the connections before replacing/rebuilding it (including the terminals of the battery itself).
1982 Mercedes-Benz 300CD
1982 Mercedes-Benz 240D - stick