Burn the pupils to make them blacker than the night. Then burn the outside dark bits of the eye, not sure the medical name for it.
You want to use the burn tool at about 15-20% opacity. Try not to overdo it, which is easily done because it can look awesome. You can then make the colour of the eye a bit more vibrant by selecting the eye area, going to Image > Adjustments > Colour balance. Have a play there and you can tweak the colour, again try and keep it subtle.
I personally wouldn't use the dodge tool on the coloured area of the eye, perhaps very lightly on the whites of the eyes to make them mega white, but nothing too much.