Evergreen trees are also referred to as evergreen conifers. They rarely require trimming, but it may become necessary if a limb dies. It's safe to remove dead limbs at any time during the growing season. Live limbs should not be trimmed if the branch is bigger than 1½ inches wide. This will promote fungal infections in the tree.
Is it Really Dead?
If the branch has leaves that are dry and brown, most likely the branch is dead. Take a knife and cut into the top layer of the bark. If it's dry and dark, your branch is dead and should be cut off.
The best tool to use for tree pruning is a saw that cuts on the back stroke. You can use pruning shears for the smaller branches. Sharpen your shears regularly to maintain a clean cut. Axes, hedge shears, chainsaws and poorly sharpened tools should not be used. They'll leave a rough cut and make it harder for the tree to heal.
When To Trim
Conifers are best trimmed when they're young. They can be trained to grow a certain way. The only reason that you should need to trim or prune an evergreen tree when it is established is to maintain it or to cut off dead branches. They're easier to trim when young because of the size of the branches. If you don't think you can do it yourself, there are professionals who know how to trim it correctly.