This is your average everyday floating anime eyeball. Note that it's a sphere, so the light hits it like it would a sphere.
This is that same eyeball with some lines drawn for where the edges of the eyelids would be-- that is, the VISIBLE eye.
Here, some flat skin tone has been added under the lid-lines to block out the rest of the eyeball, and then shadows were added to a few places, because of the change in light.
Some shadows were blocked in, following the shape of the original eyeball.
Pretty lashes were added to the lid-lines to make it look more feminine. Note that they get heavier and thicker towards the side opposite from the nose, towards the ear. Even eyes with not as many lashes will have more towards that side. Balancing towards the middle or inside of the eye will look funny.
I noticed that the right corner of the eye didn't look right with that drastic dip, so I changed it a bit, and then blended and tweaked the rest of the eye a bit.
Don't be afraid of drastic shadow! Here I took a dark orange and made a dark shadow on one side of the eye. Now it looks much less flat.
I thought the other side of the eye didn't have enough skin detail, so I worked in some dark orange shadows there too, but now the lighting is a bit hard to read again...
...so I added a little bit of blue, like there was a secondary coloured light source.
And that's about where I stopped. You could keep going, making it shinier and shinier, but since it's just a single eye, I wouldn't recommend it.
This was made in Photoshop, but you should be able to do the same kind of thing with any program that uses layers and allows for fuzzy brushes and opacity changes.