I took a fruit tree pruning course last week, and just collected my thoughts.

The essential conclusion is that fruit trees should be trained into a wineglass shape (pyramidal, with a narrow top and wide base), with 4-6 scaffold branches (Leitäste) from the trunk, each ideally dividing into roughly three upward-facing secondary branches (Seitenäste). So, 12-18 secondary branches total, all well-spaced, outward-facing, and bathed in light and air. The wineglass/pyramid shape ensures that the upper branches don't shade the lower ones, which is the other key principle underlying the whole structure. Every leaf needs light to photosynthesize, and every branch needs air circulation to resist disease. Young trees (<3-5 years) should be pruned with their eventual shape after 10 years in mind. Trees younger than three years aren’t in their prime fruiting days, so prune them more heavily to encourage strong structure. Trim mature trees sparingly to make sure their energy goes into producing fruit, rather than upward growth. Non-productive vigorous vertical shoots are called "water sprouts/shoots" in English, and should be removed; they tend to form more on the north side of the tree to seek sunlight. Fruit trees shouldn’t be great shade trees; if you would comfortably sit under an apple tree to shelter from the sun, it’s likely time to prune it back. Why bother with all this? The goals are structural integrity, long tree life (including protection from disease), energy efficiency, and maximum fruit yield.