If you're handy with a voltmeter...
First, check the battery voltage when the engine is switched off. It should be around 12.5V if the battery is good and charged.
Next check the voltage at the battery terminals when the engine is running, IIRC it should be around 14V if the alternator is working properly. If it is much lower than this (~12V or less) then the charging circuit isnt working, which would be causing your light to come on.
If this is the case, check the voltage at the terminals on the alternator (disconnect the wiring from the alternator, attatch crocodile clips to the terminals while the engine is switched off, then start it up. Keep your fingers.) This should also be around 14V and shouldnt change if you rev the engine, If not then the alternator is faulty.
If you have good voltage at the alternator but not at the battery then the fault is somewhere in the wiring between the two, follow the wires from the alternator/battery and check any connectors/terminals are tight and corrosion-free.
Last time this happened to a mate it was just a nut had come off where the circuit connected up behind the engine.
HTH Andy