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When I look at a 3D character, I'm always drawn to the eyes first. The eyes are very important, but modeling them can be a bit confusing if you're new to modeling. First of all, let me diagram the basic construction of a model eye. Some people make the pupil as a separate object, but I like to paint it as part of the iris so I can create any pupil shape that I want without altering the geometry. With this method, the eye consists of three parts: the eye white, the iris (colored part), and the cornea (clear part). Alright, now let's make the eye:
Start with a sphere, and turn it on its side. (Rotate > Z, press tab, type 90). Smooth it once or twice, we need quite a few polygons to get a good eye. The reason you rotate it is because the sphere has different shaped polys on the top and bottom, and they're much easier to make eye shapes with than the quadrangles on the sides.
See those pointy vertices? They make a strange pointy surface on objects that really gets on my nerves. Thankfully they're easy to fix. Select every other one (the inside ones) and Scale > Uniform until they match up with the other ones. Now the eye will be a little smoother.
Eyes are best textured with a UV map, and I find it easiest to UV map by materials asigned to the object itself, so select the faces where you want the iris (color) to be. Create a new material and name it something you'll remember. Make it any color, it doesn't show up on the UV map so make it whatever you want.
Select the edge loop around the iris, and loop cut. This is to make the cornea. Duplicate the new object, but DO NOT move it. Just left click. Go to face mode and asign a material to the cornea. Then Select > Hide Selected to hide the cornea, we're done with it for now. Select the iris and the eyeball, and Weld. We don't want them to be separate objects, and Weld will put them back together. (Combine doesn't do the same thing, don't forget!)
Now we're going to use a magnet. Don't worry if you've never used a magnet before, this one's easy. Select the vertex at the very center of the iris. Hold Alt and click Move > X. When asked to select an outer boundry point, select one on the edge of the colored area (it doesn't matter which one)
Right click when you've selected the boundry, and move the iris in a little bit. On real eyeballs, the iris is slightly concave, and making them this way in 3D makes them more real, and catch the light better.