Just connect a voltmeter to the starter stud and ground. Note the voltage with the engine off, then note the voltage with the engine running. You should see something about 6.3 volts OFF and 6.7 volts RUNNING. If you don't see any rise in voltage with the engine running, the alternator isn't working.
Another easy test is to shine the headlights on the garage door at night, with the engine running. Then kill the engine and see if the lights dim a little. They should dim some if the alternator is working.