Potatoes are a Spring crop which be purchased from the General Store. It takes 8 days to grow and each one can be sold for 80 G in a Shipment box.
While vanilla potatoes will spawn in the world (say in a village) you cannot harvest them. There is a bug where you can still plant them the normal way, but once again you cannot harvest them. Instead you need to purchase seeds from the general store and grow potatoes.