Pruning is the removal of plant parts, typically shoots, branches, fronds and flowers to improve health, control growth or influence fruiting, flowering or appearance. Removal of dead, dying or damaged branches and diseased and insect infested plant parts is an effective way to limit the spread of decay, disease and insects to other portions of the plant or to neighboring plants.
The first step in pruning a shrub is to remove all dead, diseased, or injured branches. Remove branches that cross or touch each other and those which look out of place. If the shrub is still too dense or large, remove some of the oldest branches.
First, prune out dead, diseased or broken twigs and branches. After studying the tree form, select the best spaced and positioned permanent branches and remove or shorten others on young trees. Permanent branches should be spaced between 6-24 inches apart on the trunk, depending on the ultimate mature size of the tree.

Removing a tree branch over 1½" diameter. First cut at "A" until saw binds, then cut at "B" 2-4" beyond "A" until the branch falls, then cut at "C", outside of the branch collar
Care must be taken when pruning palms not to cut or otherwise injure the terminal bud or the whole tree will die. Removing green fronds is not needed. However, if you wish to do so, only remove those drooping below an imaginary horizontal line drawn through the bottom of the canopy (center). Old leaves that persist on palms such as the Washington palm can be removed, as they often harbor insects and rodents and may become a fire hazard.

Proper pruning of palm trees
Fertilize trees and shrubs in the spring or fall. Make spring fertilizer applications in February or March before new growth begins. Make fall applications about 1 month after the first hard freeze. Fertilizer applied in the fall is more effective in promoting plant growth than spring-applied fertilizer. But bear in mind that unseasonably warm winter weather could damage trees and shrubs that have been fertilized in the fall. Environmentally, early spring is the best time to fertilize because it avoids leaching during the winter. Avoid fertilization in late summer (mid-August) since it may stimulate late-season growth that fails to harden off before frost.