Unlike virtually every other fruit, pears must be picked when they are still quite hard. They ripen from the core outward. As you found, if pears are allowed to remain on the tree until you can feel or see ripeness, the fruit becomes mushy and brown. Check for ripeness while the fruit is still green. If you can snap the fruit off the branch briskly rather than tugging, or if you cut open a pear and find that the seed coat has darkened from white to brown or black, the pear is ready to be picked. Once harvested, most varieties ripen in a week or two. Speed up the process by sealing the pears in a bag with a ripe apple or banana.