The formation of plant growth and then tubers comes directly from availability of the five basic needs of the potato listed here. Quite simply, with a balanced framework the plant will grow but outside that it will stop, grow weaker or die.
The soil around the roots of the plant should always be damp. The amount of water the plant needs will increase as it grows and starts to develop tubers. Tubers start to form very early in plants growth (10 inches or 25cms) so increased water availability early in the plants life will stimulate more tubers. This is a good thing for low tuber number varieties such as Kestrel but not such a good thing for King Edward which tends to make lots of small tubers. Water at night to preserve and optimise the input. Ideally keep the water off the leaves and avoid watering if rain is forecasted.
In soil this is about having well dug land that does not become flooded - it’s basically “curtains” if this happens! When preparing the ground ensure there is a sustainable drainage plan. This is usually achieved by raising the bed by deep digging and adding in organic matter. A few inches makes all the difference. Heavy soils like clays should have sand added to aid drainage. Organic matter needs to be added to lighter soils or even a mulch to preserve water. A more common challenge is container growing and too much drainage leading to water loss and the plant suffering. Ensure a rich substrate mixture is used with moisture retaining qualities.
The plant needs nitrogen in its early phase and then potash when tubers are forming. So as a guide, when the plant is in flower add a high potash fertilizer. A tomato feed is fine. Leggy weak plants are a result of too much nitrogen usually from horse or cow manures. So apply them the winter before. A good potato fertiliser can be sought from most garden centres.
Basic rules are above 13c and below 28c for effective growth, but low temperatures e.g. under 5c are not good and winds can be deceptive. So this is why we will talk about planting time as planting too early can lead to frost avoidance or damage. In the UK the last frost can be as late as May or June but thanks to global warming it’s now harder to work out! The growing bag idea has an advantage as bags can be brought inside for that one cold night. Remember potatoes do not like it too hot.
Plant in full sun or maybe a bit of shade but those in full sun will, if fed and watered, grow to a decent size and the role of the sun is providing warmth and the essential growth enabling efficient photosynthesis (the process of energy from sunlight to producing glucose from carbon dioxide and water). Avoid planting next to shaded fences or damp areas due to encouragement of disease and weak plants.