There are many ways to do the eyes. You could create eye sockets, or you could just add a flattened NURBS (or Poly) sphere (as a pupil; the whites would be textured) and just move that around along the surface.

If you really want fully formed eyes, here's what I would do:

1) Create eye sockets in the character's head in whatever shape the eyes are going to be in. This could be done any number of ways, but selecting faces around the future eye socket and deleting them, then extruding the remaining edge inside the head is the easiest way to make an eye socket.

The eye itself is best done as a NURBS sphere (because you can map an eyeball directly to a NURBS sphere more easily than on a Poly sphere), A lattice deformer can be placed around the sphere and the sphere can then be deformed to match the eye socket. Adding an aim constraint to the eyeballs is the best way (or at least the most common way) to control movement of the eyes.

The deformer should ensure that the eyes deform properly regardless of their position, though you'll want to chck to make sure you like the way the eye looks first!

Hope this helps! PS creating aim constrained eyes is relatively easy, and the procedure should be readily available online!

Regards,

Lt. Jim
NYC, USA