Each photo file is composed of three main channels - red, green, and blue. One your picture is open, it is worthwhile to try and understand why the eyes are red in the picture. If you click on the Channels tab in the channels palette, you will see each individual channel as well as the RGB channel, which is the combination of them all.
Take a minute to examine the eyes in each of the channels. In the green and blue channels, they will look normal. In the red channel, however, the eye color will look distorted and different from the other channels. Therefore, we will need to adjust this channel.
First, use the Elliptical Marquee Tool (Shortcut M) to make circles around the red spots in both eyes. After you have selected the first eye, hold down Shift and select the second eye. You might notice that a little + sign appears next to the tool. That means that you’re selecting something in addition to what you have already chosen.
With the red eyes selected, go to the menu and choose Image, Adjustments, and then the Channel Mixer. You’ll probably see Red at 100 percent. What you want to do is change the red channel to 0 percent, and change the green and blue channels to 50 percent each. You can mess around with the percentages a bit, but usually taking the colors equally from the other two channels works well.

click to enlarge
Click OK to apply the channel adjustment, and the eyes should change to a natural color. The eyes will still be selected, so use the keyboard shortcut, Command + D, to deselect the eyes.
This channel mixer adjustment can also be done on a separate layer for non-destructive editing as well. Photoshop CS3 has shortcut icons for creating different layers conveniently placed on the right hand side of the screen.