There are a lot of tutorials out there if you look up anime face modeling on youtube but usually how it works is backwards. Many anime modelers make a sort of cove/cup into the eye socket and have the iris as it's own shape within the cove instead of making a full eye shape.
You can sort of see that in these but I can't find a great picture of it. The iris floats inside a "cup" that might mess up your shaders but usually looks fine. Many MMD models work this way and end up looking fine. I'm still new to a lot of modeling and don't know if this helps but I figured I'd mention it. :) Goodluck!

(This thread is a follow-up to https://www.gamedev.net/forums/topic/698664-how-does-one-typically-model-an-anime-character/)

@Runzi333 I saw that concave / cup style eye sclera, with the floating iris in this model: https://3d.nicovideo.jp/works/td31873

It seems to work well, especially when you look at the model in profile or 3/4-view, the shape and layout really looks like a 2D drawing.