What you'll need:
The first step in drawing eyes is to draw the full eyeball itself. Draw three circles, one inside the other, each smaller than the last. These three circles will represent the eyeball, the iris, and the pupil respectively. Don't worry if you can't draw a perfect circle, neither can I! And as always... make sure to start with light strokes only.
After you have your "not-a-perfect-circle" eyeball drawn, draw an oval shape horizontally across the eyeball in the shape of an eyelid opening. This opening will serve as the frame for your eye. Try experimenting with different shapes here. Different shaped eyelids will give the illusion of different emotions/ethnicities/etc.
Once you have the opening for the eye nailed down, you can erase the lines outside. All that's left for this step is to clean up the lines a little and start getting ready for some more detail.
Now we're ready for highlights! Start placing highlights wherever the intended light source is coming from. Because the surface of the eye is wet, the highlights will be very defined, and the outer lines of the highlights need to be be clear and crisp. Also, when drawing the highlights for your eyes, remember that the eye is spherical, so the highlights should wrap around the eye instead of cutting across it in a straight line.