A palm tree grows from the center out, each new frond emerging from the center as a tight cone and then falling outwards. As new growth develops from the center the old fronds that are lowest on the trunk will turn brown, die and eventually fall off. These dead fronds are unsightly in a garden setting; this is the area that you are going to prune. Coconut palms produce coconuts, hard husked seeds that cluster at the base of the fronds. It is a good idea to remove coconuts before they become dangerous falling hazards.
Grasp the base of the brown palm frond with one hand and apply upward pressure on it. As the coconut frond responds to gravity, it tightens the stalk, making it difficult to get a knife through the tough fibers.
Using a sharp serrated knife saw the base of the frond from the underside upwards. If you are working on a ladder, be careful when the frond breaks free and falls to the ground.
Take off all the lower limbs that are beginning to show brown decay on the leaves. This is a natural process and it does not mean the plant is unhealthy.
You can prune a palm heavily without damaging it. If you want to avoid another pruning session for a while, it is fine to take off some of the lower green fronds that are only slightly brown.
Cut the coconuts from the tree using a sharp serrated knife. Make sure these heavy falling objects do not damage someone standing below you.
You can let the coconuts ripen on the tree for harvest, but be sure that you and others are aware of the potential danger.