First and foremost! Pruning a tree can be very dangerous depending on the size of the tree. There is often time a specific arsenal of equipment needed to do the job right, so we recommend seeking professional help.
The first thing to think about when pruning trees is the time of year it is. The best time to trim a tree is in late winter when the tree is dormant, so it does not stress the tree. The only exception to this rule is when you are trimming a spring-blooming tree. The best time to trim these trees is immediately after they bloom, so you do not interfere with the cycle of the next bloom.
The first thing you want to be conscious about when it is the right time to trim is to identify any diseased or dead branches.