Pears actually don't ripen all that well on trees. (They are picked when mature, but not ripe.) You'll know a pear is ripe if it yields slightly to pressure (gentle, now) applied at the base of its stem. If you have a pear that needs ripening, you should place it in a paper sack. Once ripened to your liking, pears will keep in the fridge for several days. Just keep them out of plastic bags when storing.