It is common practice to augment data (add samples programmatically, such as random crops, etc. in the case of a dataset consisting of images) on both training and test set, or just the training data set?
Only on training. Data augmentation is used to increase the size of the training set and to get more different images. Technically, you could use data augmentation on the test set to see how the model behaves on such images, but usually, people don't do it.