Cherries are at their delectable peak right now, so it's easy to choose flavorful, sweet ones. Select by color and feel: you want cherries that are dark for their variety, glossy, and not soft when you press them. Plump is good, but mushy is not.
Once home, keep cherries in a covered bowl or container in the refrigerator and they should last about a week. As is true with all produce, don't wash them ahead of time: wait until you are ready to eat them.
For a variety of recipes using fresh cherries, see 7 Ways with Cherries.