Clean clippers by removing any old dirt or rust with a damp cloth, and cleaning the blades with a bleach-water solution of one part bleach mixed with nine parts water. This ensures your clippers won't spread disease around the yard, and gives you a better cut. Thoroughly dry the clippers before using them on your tree.
Remove dead or diseased limbs from the tree first, followed by branches growing laterally that might compete for dominance in the tree. Use hand sheers for branches smaller than 7cm, a chainsaw for branches thicker than 10cm and pole pruners for branches high up in the tree.
Cut some of the upper, center-most growth from the tree to allow for better light inside the tree. "Thinning the crown" allows for better airflow, reducing the likelihood of trees getting damaged in high wind.
Remove any limbs growing near the bottom that may alter the overall shape of the tree or pose a risk to people beneath the tree.
Discard of trimmed branches in the compost pile, send them to the wood chipper or dispose of the branches according to the restrictions of your municipality. Don't let diseased branches remain near your tree too long.