Pick a shape for the eyes. Real eyeballs and irises are round, but anime style irises often vary in shape, and ovals are common.
Draw the pupil.
Pick a light source. Be careful of chosing the same as on the other parts of the base.
Apply a white highlight accordingly to the light source. This light can go over the pupil: it is the direct impact of the light on the eyeball.
Brighten the area at the opposite of the white highlight: the eyes being translucid, the light goes through them and brightens the irises.
Eye shape
Draw the outline of the eye.
(Optional) Use a pale color - pale gray, blue or violet, for example - for the white of the eye: eyeballs are not naturally white.
Add the shadow of the lids and eyelashes over the iris and eyeball.
Add a white highlight on the eyeball.
Eyelids and skin
Add the basic skintone and the eyebrow shape.
Depending on the size of the eye, pick one (small) or two shadow tones (large) between the basic skin color and black.
Soften the borders of the eye using the shadow colors, to produce a soft gradient effect.
Make the lower border lighter, as the lower eyelashes are small and thin.
Add the eyelashes shadows on the skin, and use the shadow tones on the tip of each eyelash, to give the illusion that they are getting thinner at their end.
Shading
Pick another shadow tone to use on the skin.
Draw the eyelid and the corner of the eye.
Start shading the skin: use a thin shade just under the eyebrow, as well as over the lid line to enlarge the crease it makes.
Lights
Pick a brighter color for the skin, and start applying it on the parts exposed to the light, or more reflective. (The forehead, the lids...).
If necessary, use a pattern to soften the shadows.
Finishing touches (Optional)
Add a more vivid highlight to the top eyelid.
Add a red/pink tone to the lower lid border, as the skin over the bottom eyelashes is pink, and add the small gland at the corner of the eye.
Darken the first third of the eyebrow, as it enhances the ways it becomes thinner.
Correct the shading if necessary, soften the remaining aliased parts.