The best way is to drive it to your nearest auto parts store and have it tested. You can test it somewhat yourself. Start the engine and use a volt meter to test the voltage that is being supplied by the alternator for the battery. If it is less than 13.5 volts the alternator is bad.
How to Tell If Your Car Alternator Is Bad Check related link below…
you could pull off your positive battery cable if it stalls out then you alternator is the problem
A bad belt, a bad regulator in the alternator or bad brushes in the alternator.
Start the car, unplug the battery the alternater should power the car. If it dies the alternator is bad. You can also get it checked at any parts store.
The quick easy method for determining a bad alternator or at least to find out if it is charging, while the car IS running remove the negative battery cable from the battery, if the car stalls then you need to have the alternator service inspected.
Get engine running. While the engine is running disconect the POSITIVE termninal from the battery. If the engine dies, the Alterntor is bad.
Perhaps thids might help... http://wiki.answers.com/Q/How_do_you_tell_if_the_battery_or_the_alternator_is_bad
bad alternator, bad voltage regulator, bad battery, bad connections.
Start engine and measure volts at battery, it should be at least 13
The alternator is belt driven and so is the water pump but that is where the correlation ends. There is no way a bad alternator could cause a water pump to go bad unless the alternator pulley was warped. Then there is a small chance.
alternator is bad
Take the belt off and spin the alternator by hand. If you hear a grinding noise, like sand rubbing on metal, its probably going bad. Also try to wiggle the pulley up/down/left/right. If it wiggles, the bearings are going bad. Of coarse you can always wait until they get so bad they shatter and the alternator wont spin at all, like i did. :(