This tutorial will present two ways to get rid of red-eye in digital pictures. My tool of choice is The Gimp and this presentation assumes you will be working with that tool.
The example picture for this tutorial is much larger than the versions displayed in this page. I will show cropped versions for presentation purposes.
First Method: recolor the problem pixels using acceptable colors from nearby pixels.
The technique of this method will be to use a color already in the picture and use it to affect the pixel colors that are showing so much red.
The first thing to do is to zoom in real close to the eye you want to adjust. Then, select the eye-dropper tool from the Gimp toolbox. Choose (click) a pixel color from the image that you believe would make a pretty good color replacement for the redness of the eye.
I have noticed that the best colors for red-eye repair come from other portions of the eye. Eye pupils aren't really jet-black. They are a little darker than the surrounding area. Also, I have noticed that the pupils are a little bit red; so totally getting rid of the red doesn't look very natural. Your goal will be to get rid of most (but not all) of the red.
In this example I have selected a pixel that is dark but still natural to the eye color.
The next step for this method is to bring up the pen tool. Bring it up with a double-click so you can work with its Tool Options.
The size is almost certainly going to be too big.
I recommend setting the pen size to be smaller than a pixel. Then you can click on a pixel in the red-eye section and cause a partial blending of the pen color and the red-eye pixel color. So, with a couple clicks you can get a nice blend of the red-eye color and the new/replacement color. Remember, you don't want to totally get rid of all the red but to lessen it so that it looks more natural. Here is the result of my quick effort on one eye. The other one remains un-retouched:
The above method is pretty quick and straightforward. The next method is just as quick but a little more difficult to learn. I think it has somewhat better results too.
Second Method: Burning the red layer
First step in this method is, again, to zoom in real close to the eye on which you are going to work. Then, right-click the image. Select Dialogs and Channels.
You will have a new dialog that shows the three color layers of your image. You want only the red layer to be active. You can deactivate the other two by clicking on them (not on the eyeball; but on the line that labels the layer). When you do any manipulation to your image you will be doing it to the active layer(s).
Now select (with a double-click) the Dodge/Burn tool.
You will almost certainly need to select a different Brush since the default brush is pretty large. Set the size so that you will be convenient to use it to burn in the redness but not surrounding areas that need no burn.
Set the Type to Burn (obviously, you want to darken the area and not lighten).
With mouse strokes, paint over the red area with the Dodge/Burn tool. At some point it should look the way you want.
In my example I went ahead and worked on the other eye too and I kind of didn't like how a few pixels went bluish-purple colored.
So I deactivated the red layer and activated the blue layer. I did a little burning over the bluish-purple area and finally had the result I wanted.
Now the eyes are more pleasing to my own eyes.