Er..not entirely sure what I'm talking about, but here's something that might help as done quickly in paint.
To do a basic anime eye as I know it. You draw a circle, then dot the center. and draw a shine or two to the sides of it however you want. Then, you shade in some as you see fit or leave it open. Usually shading gives either a more realistic look or gives a a bit of a darker appearance. Not shading can look a bit more cartoony or make someone look like they have clearer eyes. Then you make the lines around the eyes to frame the eyelids. Bigger, more open eyes seem younger or more innocent. The smaller and squintier, the more jaded or old. And, occasionally, completely squinted eyes can mean that someone is perverted or extremely happy and carefree. Or that they don't have eyes...
Anyway, after framing the eyes, you erase the circle outside the lines and add on details like eyelashes.
The other method is simpler, but usually used on more children's shows or stuff with a younger audience. I saw alot of this kinda eye on the first season of Digimon and on Pokemon. It's usually a large oval with some manner of black dot or line in the center and the eyelid lines around it. Eyelashes and whatever are added and, presto.
If anyone has anything to add...correct...etc...