Depends if they are an early or a main crop potato. Early potatoes will only keep for a few weeks. Main crop if properly stored will keep for several months.

Assuming they are main crop when you lift them do so, if possible, on a sunny day and leave on sitting on the soil to dry off the skin. Brush any soil that is attached to the potatoes off gently. Store in either paper or jute potato sacks in a cook, dry and dimly lit location. Don't let them get frozen in winter. Check regularly from October time on for potatoes that are going bad and put these in the wheelie bin.