Never remove more than 1/3 of a tree's crown.
Where possible, try to encourage side branches that form angles that are 1/3 off vertical (10 o'clock or 2 o'clock positions).
For most species, the tree should have a single trunk.
Ideally, main side branches should be at least 1/3 smaller than the diameter of the trunk.
If removal of main branches is necessary, cut them back to the trunk to avoid leaving stubs.
For most deciduous (broadleaf) trees, don't prune up from the bottom any more than 1/3 of the tree's total height.
Rules for Pruning