Cut a piece of carpet that you are going to use in order to patch damaged areas in the carpet. Make sure that the piece of carpet you cut is at least a couple of inches larger than the damaged area on all sides.
Now it comes to preparing the carpet patch that you will be using to repair the damaged area. Place a circular metal lid on the piece of carpet from the earlier step. Along the boundaries of the lid can, cut the carpet with a utility knife. Try to be as neat as possible while cutting. When you are done, you will end up with a circular patch of carpet.
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Place the same metal lid on the damaged area. Make sure that the lid completely covers the damaged area. Cut along the boundary of the lid with a sharp utility knife. This will create a circular hole in the carpet. Apply a layer of adhesive material using. Place the circular patch you made in the earlier step to fill the hole in the carpet. Firmly press the patch downward and wait for the adhesive to dry.
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By patching it up, you have successfully repaired one of the areas where the carpet was damaged.