"Red eye" happens when the light from the camera flash reflects off the subject's retina. It can make for a disturbingly demonic image.
i. Open the Image
Select File, Open or click the Go to Bridge icon in the Options bar to launch Bridge; then open the file you want to modify.
ii. Zoom in Close
Click the Zoom tool in the toolbox or repeatedly press Ctrl++ in Windows or 
++ on the Mac (the Ctrl/ key and the plus key) to zoom in tight on the subject's eyes.
iii. Select the Red Eye Tool
Select the Red Eye tool from the toolbar. You'll find it nested with the Spot Healing, Healing, and Patch tools.
iv. Click in the Red
With the Red Eye tool active, click in the red area of one eye. If the correction doesn't match the size of the pupils or seems too light or too dark, undo the effect and change the Pupil Size or the Darken Amount setting on the Options bar and then reapply. When you're satisfied with the result, click in the red area of the other eye.
v. Evaluate the Results
The final result should look natural, not drawing attention to itself in any way.
Fixing Non-Red Eyes
Many animals have a special reflective layer at the back of their eyes to help with their night vision. This can cause green or white eye instead of red eye. The Red Eye tool looks for red, so it isn't of any help if you want to correct green or white eye. Instead, use the Sponge tool set to Desaturate to remove all the color from the affected area and then repeatedly apply the Burn tool to the area, set to Midtones.