The name "fir tree" actually encompasses a wide variety of evergreen trees, all of which fall under the "coniferous" type. Fir trees are typically conical in shape -- the best-known fir tree being the stereotypical Christmas tree -- and their branches are lined with evergreen needles rather than broad leaves. Fir trees are unlike other coniferous trees in that they have a "dead zone" behind the green and growing branches. The dead zone comes about because of the dense foliage of the fir tree, which produces severe shade in the tree past a certain point, which in turn kills off any new buds in the dead zone. You only want to prune in the green zone to keep the aesthetic appeal of the tree intact.
Put on your work gloves to protect your hands from the fir tree's sharp needles, then examine your tree to determine where the dead zone begins. Take careful note of where the dead zone exists, as you do not want to make many pruning cuts into this zone, unless the entire branch is dead or diseased.
Locate any dead or diseased branches and remove them from the tree where they connect to the trunk. Use your cutting tool to remove them from the tree.
Examine the live zone for branches that, when completely removed, will not affect the aesthetic appeal of the tree. These branches can be removed completely from the tree in the same manner as you removed the dead or diseased branches.
Make thinning cuts in the "live" zones. Make sure when you partially remove a branch that you leave a green shoot at the tip of the branch, otherwise the branch will have no way to continue growing and will wither and die. The shoot you leave will experience explosive growth in the next growing season, so make sure it is located in a position where it will look good.