My 2 cents: I do eyes, it's just kinda...comforting to me and creepy to others (both are good things from here
) This is how I learned. It's kind of involved, and it IS a technique for teaching yourself and there are probably easier ways
Study close up pictures of eyes (particularly irises, I did this by staring at friends and my eyes intently. DO NOT stare a strange dog in the eyes!!! This is potentially DANGEROUS) and paint them as anatomically as possible, disregarding all reflection for now. Study the anatomy of the eye, how it's put together and how it sits in the skull. I saw a cow eyeball dissected, and pull from that knowledge in small ways. Understand how light works and how eyes see.
If you know all that, you will know things like how thick the clear bits are, how eyes are colored and therefore how they will look in different lights. It's really cool, actually.
If that's too much work (and I absorbed that information throughout my childhood so it may be impractical) My method of drawing eyes is as follows:
1. Draw eye opening shape
2. Draw orb of eye within
3. sketch in highlights carefully
4 Draw iris
5. draw pupil
6. sketch in shadows
7. shade color into iris, a little bit at a time.
Animal eyes, things to remember: They DO have whites in their eyes, often these are hidden sometimes they aren't. Eyes are Orbs. Shape of the pupil, check out how it gets bigger/smaller so you can draw in lines of the iris to add life.
Draw, paint, draw, sketch, draw draw draw to get them right. Remember you don't need to sketch the whole animal to practice the eyes!
I could probably say more, but I've babbled enough for now.
Peace!
Irry
I've a friend here who hails from Byron Bay, although she's been in the States for some years now. 
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