You can remove red eye by selecting the tool in the Touch Up menu under Eyes. If you try the tool and find that the red isn't going away, there are a couple things to try.
Make sure you have the right layer selected. Open the Layers palette at the bottom of the Editor (the 3 stacked squares icon) and select the photo layer that you want to edit.
Try zooming in before using the Red-eye Remover, especially if your photo is small or low resolution. The more area you have to work with, the better. (If you are editing a picture of a large group of people taken on a camera phone, you will have a trickier time than if you were editing a professional headshot, for example.)
If Red-eye Remover is STILL not working for you, try this work around:
• Zoom in (you can adjust that with the plus and minus signs displayed in the bottom right of the Editor) to increase the eye area you want to edit. After using the Red-Eye Remover tool, try the Eye Tint tool by selecting the appropriate eye color and brush size. You'll want to be very generous with the fade to retain a natural look. Erase any errant color strokes with the eraser tool by clicking on the Eraser icon.