Messing with eyes is very dangerous.  If you get it a tiny bit wrong, it can look horribly bad.  So please tread cautiously if you need to do this.

A while ago I was asked for help to move the iris on this photo:

First, I selected the inside of the “good” eye, copied it to its own layer, flipped it, and moved it over.  Then rotated a bit it so it lined up:

Then added a mask and carefully masked it in:

It was a bit too bright, so I used a Hue/Saturation layer to slightly darken it:

Then I copied the other eye again, onto its own layer, and moved it over the top.  Of course I didn’t flip it this time, because the catchlight needed to be on the correct side.

And finally, masked that in too:

Here’s the final before-and-after comparison: