So, starting out. Finish everything else first. I once did the eyes before the wash on the skin and, well Rockbottom got redeye.
Step 1, paint black on. This doesn't want to be just in the actual eye, around it slightly too
as this gives it some definition. Don't go mad though, otherwise you get a panda.
Step 2, Put the white in. This does want to be just in the eye. Leaving just a bit of black around the edge. If you go over don't sweat. Touching up is easy.
This next part is honestly the part that I see most people do wrong and end up with crazy boggle eyes. Don't paint the pupils as dots. Just don't. First off you will never get them to be looking in the same direction and secondly, it doesn't even look natural even should you manage it. Instead paint a line, from the top bit of black right down to the bottom. It is easier to get them in the right place and it looks more natural.
Now I don't claim to be an expert and doing something like this is pretty odd for me as a pretty slapdash painter. But hopefully it'll help at least one person out there.