The Eastern Red Cedar is not, technically, a cedar tree at all. It is a Juniper. As such, it is important that you do not trim too much at a time. Trimming back to brown wood or brown leaves can leave a bare spot in your tree that will not recover for possibly several years. Also keep in mind that Eastern Red Cedars can grow to a height of 100 feet or even more, so if height is a concern, you will need to top your tree regularly.
Remove all vertical branches that appear to be competing with the main trunk of the tree. There should be only one trunk, and this frequently means cutting off competing vertical branches. Cut branches 1/2 inch from the main trunk using the 3-cut method if branches are more than 1 1/2 inches in diameter. Start by making a cut halfway through the branch from the underside approximately 3 inches beyond where you want the final cut to be. Cut all the way through the branch from the top side approximately 3 inches farther out than your first underside cut. As you cut through the branch, it will break off at the first underside cut, preventing the bark from being stripped away. Cut off the 6-inch stub and the branch will be cleanly cut.
Cut all low branches that interfere with walking around the tree.
Cut all branches that grow toward the ground.
Shape your tree into a basic pyramid shape by leaving lower branches long and cutting successively higher branches slightly shorter. Cut the tips of the branches, being careful not to cut back to brown wood or brown leaves as these may not turn green again.
Top the tree if necessary. Cut up to 1/4 of the tree's height off the top of the tree.
Water well after trimming.