Sometimes picking fresh fruit can be a mystery. But it should be easy to pick ripe apricots at your grocery store or farmers' market. You just have to know what you are looking for. First, know when the apricot season is in your area. It is usually from May to August. That will help you know whether to look for your fruit in the produce, canned goods, or frozen section. Of course, for the best apricot flavor, you want to use the freshest you can find. You want to choose apricots that are firm but plump with a deep yellow/orange color. Do not choose any that are yellow or greenish-yellow. You also want to stay away from those with bruises, cuts, and shriveled skin.