This tutorial shows you a fairly easy way to fix the pet eye problem simply by painting over the problem part of the eye in your photo-editing software. You can follow this tutorial using any software that supports layers, though I am using Photoshop Elements for these screen shots. You should have some basic familiarity with your software's paintbrush and layer features for working this tutorial.
My dog Drifter, and my sister's cats, Shadow and Simon, have agreed to help us out with this tutorial. Feel free to copy the picture here to use for practice as you follow along.