What is the easiest way to remove the papery covers from the peanuts?
Here's someone with a lot of experience doing it! video

Dropping the peanuts into boiling water for a couple of minutes, then draining and rinsing in cold water is supposed to make them easier and quicker to peel.

I've heard freezing them overnight helps.

One method method that I have actually done is to peel them by rubbing them with a towel while they are still warm from being roasted. The trick there is to only roast small batches at a time so you can get to them all before they cool.