jim

generally when you put a meter on the battery you will get static voltage (example:12.7v)
then once you start the engine and rev it up the alternator should kick in somewhere just over idle speed and start recharging the battery, you should notice it start to climb.
Lets say after you start it it starts out at 12.7v, then start the engine and it may drop some to lets say 12.3v.... then once you rev up the engine it should jump to lets say 13.2v and will start climbing from there.

as a general rule a normal charging alternator should charge between 13.2v to 14.8v, anything between that is considered satisfactory.

Since you say the meter is not changing when you start the engine tells me there is something wrong with the alternator, is why the light is on. Even if it is charging a little bit there is still something wrong inside the alternator making the light come on. Also could be a loose belt or worn pulley causing it to slip, check that first.