When the potato leaves have grown to about 10-15 cm in height, it is a good time to "cup" the potatoes. This means that you push up soil around the tops from both sides. In this way, the potatoes do not end up too shallow. My hoe is perfect for this job. I also usually put grass clippings from the lawn around the tops. Then I get in bonus fertilization.
So, when can you really start harvesting potatoes? When the potato plants have bloomed, I usually start harvesting my potatoes. However, there are some varieties that do not set flowers. Then you simply get up a couple of seedlings and see if the potatoes are big enough.
Enjoy!