|The Redeemed Gardener|
Well, it all depends on what you are wanting. If you want “new potatoes”, small, immature potatoes, you should harvest them before their vines die or earlier in the summer (around the first day of summer). They will be about 1 to 2 inches in size.
If you want mature potatoes, or “late potatoes,” (as Grammie called them) you should harvest them in late summer/early fall. Just wait for the vines and the flowers to die, and then harvest the potatoes at full maturity.
Here's another method we used, If you have a lot of plants, you can harvest some of the plants earlier in the summer and get “new potatoes” and leave the rest to dig up later. Just experiment and try digging some at the end of July, some at the end of August, and some at the end of September. Then next year, you’ll have a better idea about how big they are at what time of the season.
When you go to harvest your potatoes, here is an article that I posted a while back on a cheap Mini Root Cellar. "Cool, Cheap, Mini Root Cellars"