What is the fastest way to reduce a swelling of the eye from an injury?

Black eye? If you are referring to swelling around the eye, then ice or cold will help. If the eye itself is swollen then it could be more serious and needs evaluation and probable medications.
Rest and coolness. After injury, the tissues around the eye can swell dramatically. If there is no bleeding in the eye, using nsaids can help relieve inflammation. Using cool compresses may be helpful as well. Sometimes, sleeping in a recliner can keep the head higher and reduce swelling.