Red-Eye occurs when a photo is taken with a flash that is too close to the subject. This is very common for on-camera flashes for that reason. To avoid the problem altogether, try using a larger flash such as a speed-light. Or, photograph in natural Light instead.
Click on the Spot Healing Brush Tool and go down to the bottom of the menu to select the red-eye Tool. This Tool works best when set to a 50% pupil Size and a 50% Darken amount. Click and drag around the eye, and let go. Voila! That’s all there is to it, folks.