Normally, tree-ripened fruit is considered to be of best quality and flavor. However, pears left on the tree to ripen become soft and mealy in the center and so are picked green and hard. Once picked they ripen at their own pace at room temperature. My mother would lay them on a bench and cover with a layer of newspaper to keep out the light. Daily she selected the ripened pears for use.
Most pears are ready to eat when they yield slightly to pressure next to the stem.
Some show a slight color change, many remain green when ripe. Consider how pears are to be used when selecting. Salad pears should be ripe and juicy. Under-ripe fruit may hold its shape better when cooked and may require slightly longer cooking time than stated in the recipe. Cook pears without sugar for sauce but with sugar to retain the shape of slices.