First remove all dead and diseased wood from the peach tree. Then cut out all branches which are growing inwards. Try to find around five fruit-bearing branches, spread around the trunk. These should branch out so that together they form a loose crown on the peach tree, with nothing in their way. After pruning, focus on shoots and healing wounds on the tree, and gain experience for future pruning operations. Or, as the gardeners' saying goes: "If a fruit tree has been pruned properly, you should be able to throw your hat through it".
When pruning peach, particular attention must be paid to the difference between real and false fruit shoots. Only real ones will bear high-quality fruit. Don't worry, it's not that complicated:
False fruit shoots have a couple of leaf buds at their base (pointed buds) but have mainly flower buds on the branch (rounded buds). Cut these false shoots down to two leaf buds. These will then grow out and form, for example, another false shoot and a real shoot. Again, cut the false shoot back to two buds and allow the real one to bear fruit.
Real fruit shoots have one pointed bud on the left and one on the right of them. These shoots form worthwhile fruit-bearers, which is why it is important to promote the real fruit shoots when pruning the peach. If necessary for crown formation, it is possible to shorten these. Otherwise leave them to bear fruit.
After harvesting, cut the real fruit shoot back to the branch nearest the trunk, which it formed during the summer. Then trim this remaining branch back to two buds. If these buds grow again later, check whether they have formed real or false fruit shoots and proceed as described.