To create eyes you will want to take the time to properly construct them. This is the way I create eyes but of course doing it this way is entirely optional. There are a variety of ways to make eyes for plush toys. My method is by sewing. I do all my eyes by hand and it does take a lot of extra time. The reason I use felt is because it has the same type of fiber as yarn. Felt can be made from wool or any other type of protein fiber. I found as a personal preference that machine applique eyes don't fit right for me. But that does not mean it wont be right for others.
There are a ton of tutorials on how to do machine embroidery by just doing a search on google.
There is another method on making eyes that uses your printer. I have not tested this method myself but have read many reviews on people using it and they seem to like the results http://www.youtube.com/watch?v=7CnTljGcuJM&feature=youtu.be
Cut out your pieces by tracing the eye. You will want to make a cut out for each color. This site has a neat method for cutting eye pieces http://needlepointstudyhall.blogspot.com/2010/04/glad-press-n-seal-tutorial.html
Now set those pieces aside and work from the bottom up. Try to match the thread colors.
Next place the next color making sure to line up the edges. Try to keep the bottom color from showing if that is what the picture tells you.
Pinning your felt pieces as you go can help you see how you are progressing. This also helps keep your pieces from flying away
Now you have your finished eyes. The next step is to sew them to the toy. Pick a color similar to the toy but not so dark that it can show through your eyes. I usually use black since my bottom layers are usually black anyways.
What you want to do is sew in the eye as firmly as you can. If you are unsure if your eye is secure enough you can lightly tug on it and see if it is coming lose.