Eyes are window to the souls.  This is very true.  No matter how cool your design is, if the eyes don’t look lively, the character would always look odd and creepy.  I call it the sad dead eye syndrome.  So knowing how to paint eyes is a really important skill.  There are many ways to render/paint an eye; And this is the technique that I use to paint CG believable eyes.  

As always, Think simple!!!!  Break it down to the essence and use layers to help you out.  

First, know your LIGHTSOURCE.
The more you know about where/type/angle of your lightsource, will determine how to render the eye.

Second, break things down into BASIC PRIMITIVES.  The sclera is basically a semi-gloss sphere; and the iris is a glass sphere because the cornea is basically a glass dome.  

Third, add details and real life logic to make it believable.  Edges and shadow always help makes things look believable.

I attached a gif to show you the order how I usually paint an eye.  And I also attached a painting I did for DreamWorks the three Diablos as an example on how I use this technique for my visual development work.  Try it out, experiment and have fun.