To treat a black eye, apply something cold to the affected area; it helps to reduce swelling and it constricts blood vessels, which in turn stops the bleeding below the skin. Make a crushed ice pack or grab a package of frozen vegetables and apply the compress to the affected area for 10 minutes at a time (10 minutes off) to prevent damage to the skin around your eye from the ice.
Besides icy treatment, there's not much that can be done for a black eye except avoid doing anything that could cause further injury, such as putting pressure on the swollen eye or trying to force it open. If you need a pain reliever, take aspirin or acetaminophen (Tylenol, for example).
A doctor will recommend treatment with a cold compress to reduce swelling and stop the bleeding.
However, you won't be able to determine the possibility of eye damage by simply looking in the mirror. If the eyeball itself is damaged or if vision is affected, see an eye specialist as soon as possible after the eye trauma.