Yesterday was the 1st time I had the Chevelle out in weeks because of the sh***y weather. Drove 30 miles to a friend's house for a gathering and when I got home the car wouldn't start and the volt meter was only showing 10 volts although the car ran fine until I tried to restart it and got it started by rolling down our little hill and popping the clutch in reverse. I take this as giving the alternator a clean bill of health. Hooked up the trickle charger and I just checked the battery, an almost new red top Optima, and it had a full 12 volts. Started the car and revved up to about 4500 the volt meter slowly drifted from 12 to 11 usually it would have gone up to 14. Shut down and checked battery and it was down to 11.8 volts. What is the logical process of elimination to troubleshoot?

What year car?

I suspect the alternator or regulator is not working properly.
Check the voltage at the power distribution point. That where the regulator monitors to determine what to do. You should get about 13.8 volts at that point.

If it is below 13.8 check the alternator and regulator for proper operation.

You can take your alternator to an automotive electric shop and have them check it. They may charge for the service.