The eyes are the window to the soul, so it is important that eyes are as good as possible when modelling and animating characters, so create the geometry of the inner eye to get better results.
The white material has a high specular value around 240 and glossiness of 80, then use a Raytrace map on reflections with a value of 20.
Copy this material for the Cornea but reducing the opacity to 0
Create a 100% self illuminating black for the pupil and apply a bitmap for diffuse and specular for the iris.
Group the eye and adjust the pivot point to the centre and apply a look at constraint to a dummy object to rig.
Adapted from

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