Pineapples do not ripen further once they are cut from the plant. Most pineapples available in grocery stores are already ripe, even if they have a light green tinge to their exterior.
In order to tell if a pineapple is fully ripe, one should try smelling it. The sweeter and more aromatic the scent of the uncut fruit, the more ripe it is. It is also important to check the exterior of the fruit for mold prior to purchasing it. After cutting and coring the fruit, it should be stored in an airtight container in the refrigerator, as pineapple spoils quickly if it is left out on the counter.