First, if you're using artificial lighting, be sure to have lighted the eyes properly. If you get the light enough toward the front (without being fully frontal and flat) so that the light enters the cornea at the right angle, it will brightly illuminate a crecent-shaped area of the iris opposite the catchlight.
In addition to that, there are some standard "cleanup" tasks I perform on eyes:
1. Clone out veins.
2. Use the lasso selector to select the white areas (all at once, not one at a time), then desaturate them about 40 percent to lessen any red or yellow cases, and brighten them very slightly (set brightness to 3 or 4). The desaturation is more important than the brightness--a healthy young eyeball is light grayish, not red, yellow, or bright white. Make sure you don't remove any of the corner and lid shadows that give the eyeball its spherical, lidded appearance. Eyeballs need spherical shading to look properly round, and eyelids have definite thickness that normally casts a rim of shadow on the balls.
3. Remove fill flash catchlights and any other catchlight clutter (secondary windows, et cetera). A clear, clean single catchlight makes the eyes look clearer and cleaner.
4. Often the eye closer to the main light will have a larger, brighter catchlight than the opposite eye. I'll copy that larger catchlight and paste it over the smaller one--very carefully, because the slightest misalignment will make the eyes look like their pointed in different directions (this is also a way to subtly correct eyes that actually are looking in different directions). Usually I copy the entire iris, paste it at a lower opacity to get the pasted iris registered precisely over the original iris, then erase away the unnecessary parts of the pasted iris.
5. Enhance the illumination of the iris. I mentioned that a properly illuminated iris will have a crecent-shaped bright area opposite the catchlight. If it's not there, I'll put it there. But you have to be careful with brown eyes--you can't just dodge a clipped brown eye lighter. You have to get some semblence of the natural texture of the iris into brown eyes. I set the clone tool to about 40% opacity and then clone from the eyebrows to create the crecent shape. That gives me some of the texture that makes it look more like an illuminated brown iris. Yes, you can probably find brushes for that, but I find that a 40% skin-tone-plus-hair brush is instantly available from the eyebrow.
6. With lighter eyes I'll lasso the irises (both at the same time) and apply curves to lighten the lighter tones and darken the darker tones, that is, increase the internal contrast. Then while the irises are still lassoed, I'll sharpen them a bit. I prefer using curves rather than burning in tones that aren't really there.