Open the photo where the person has a red eye that you want to remove.
Now select the Red Eye tool from the Toolbox (it's nested under the Spot Healing Brush, or you can use the shortcut by pressing Shift+J a few times.)
Now you use the Red Eye tool just like how you use the marquee selection tool, just draw a selection around the red eye, and it will instantly remove the red in the eye.
If you don't like the result, there are 2 options in the Options bar that you can adjust:
Pupil Size: The higher the amount, the more colors it will select, so if your first try doesn't select all the red, increase the Pupil Size.
Darken Amount: Determines how dark the color is that replaces the red eye, the default 50% gives you a very dray gray pupil, if you want a pure black pupil, just increase the amount.