Sort through the blackberries in question, removing any that are partially or fully red or green rather than completely dark. These berries are not fully ripe and will not be sweet.
Examine the remaining blackberries, looking for any that are partially shriveled or overly soft to the touch. These are overripe and will not have the brilliant sweetness or familiar hint of tartness that a perfectly ripe blackberry should have. Remove these blackberries from the batch and discard them.
Search through the blackberries, removing any that have visible mold. This will generally be an obvious section of powdery whiteness. These will not taste appropriately sweet.
Smell the blackberries. Unripe blackberries have little to no scent, while overripe blackberries smell cloyingly sweet with a hint of rot. Perfectly ripe blackberries smell very similar to the way you would expect them to taste: sweet and intensely fruity.