[J-Ri]

I second what j cAT said, except an alternator charging as low as 13.5V will charge the battery sufficiently. In some cases (but usually on toyota and nissan) as low as 13.1V is all it will put out. Ideally it would be closer to 14.5, but it may not need an alternator based soley on a lower voltage output.

Never check the alternator by disconnecting the battery. It can damage the alternator's insides when it is reconnected.

One more test to do is to turn everything on. High beams, 4-way flashers, radio, windshield wipers, rear window defrost, everything. Run the engine at 1500-2000 RPM and make sure the voltage stays above 13V. This is to test to make sure that the alternator can keep up with a higher amperage demand.

Yet another test is to put one lead of your voltmeter on one battery terminal and put the other next to the other terminal (but only touch the plastic case, not the terminal). If the meter reads any voltage, clean the battery and terminals with a mixture of baking soda and water, and then rinse it off with plain water. If electrolyte leaks out the vents, it basically forms a big resistor on the battery case, which can kill the battery in only a few days.