In general, I like to leave the root end on, so I can use it as a grip when slicing or grating it.
For just a few cloves I do it by hand, I just pinch the clove between thumb and index finger enough to get it to separate at the root end, then use mt fingernails.
For large amounts to be used right away, shaking the cloves in a container works well. But this can bruise it, so I don’t like doing it for pre-peeling garlic for later use.
To pre-peel, I take the cloves of garlic and soak them in warm water for 30-60 minutes. After rehydrating, the peels slip right off with practically no effort. This is gentler, so the cloves can then be dried off, then stored in the fridge in a baggie lined with paper towel, or in a container. As long as the cloves are undamaged, they keep for weeks.