Most dogs (but not all) have dark eyes which are usually brown. This is the example I will use for this demonstration.
First I start with the pupil painted black. The 'white' of the eye is based in pink since is usually more pink than white. Don't forget to include a tear duct. I've floated a grey around the eye.
Next, I've drybrushed the brown of the eye. I find that something like Burnt Sienna works best. Drybrushing gives a much softer look to the iris. I've left the outer edges and pupil black.
I've made the rim of the eye and tear duct appear wet, by floating and then highlighting with bright highlights of white using a liner.
In the pink area, I've darkened the areas where it meets the rim of the eye and lightened the middle area.
For this example, I've used light in the eye that shows the dog is outdoors. This is why there's a blue float near the top of the eye (it's a reflection of the sky).
Of course the sun in the sky is brightest and will reflect as a white dot. Notice I've made it a bit soft rather than a 'dip dot' with a stylus.
I'll be giving the dog some lashes which will cast a shadow on the eye, so I've painted that with black on the top of the eye. Then I've added lashes in several shades of grey with a liner - notice the placement of these!
Hope this little demo will help you the next time you are painting eyes!