Peach trees require heavy pruning to ensure good fruit production. Pruning should be done during winter when the tree is dormant.
Generally the tree should have a funnel shape - open center and sloping sides to allow sun and air circulation. First, remove dead branches. Then remove crossing or rubbing branches. Then, remove any branches which have born fruit - these will not bear fruit again. Next, thin branches throughout the tree to ensure even branch growth. The tree can be maintained at a height suited to your garden, but keep the tree short enough that you can reach all the fruit even that on the top of the tree.
Fruit is produced on the twigs and branches that grew the previous summer, ie 1 year old branches. These branches should be headed back by about one-third.