After you’ve found the image and clicked it to select it, choose the “Edit” button in the lower-right corner of iPhoto’s window.
Within Edit mode, click on the “Fix Red-Eye” button on the right. Then you’ll see what options you have:
If “Auto-fix red-eye” is available, you can try using that; however, I’ve found that it doesn’t do a great job, so I usually toggle it off and do the repairing myself. Then what you’d normally do here is adjust the slider to get your circular cursor to be the exact size of your subject’s pupils. Here’s the thing—it’s difficult to judge the size of things while you’re moving that slider, so you’ll end up going to the pupil to measure, adjusting the slider, going back to the pupil, and so on, until you kind of wish you could give someone a black eye instead of a red one.
There’s a better way, though—position your cursor over a pupil, and use the left and right bracket keys to adjust the size of the cursor.
Then you’ll click each pupil to apply the correction.
Um, that’s gonna be kind of hard on a cat picture, isn’t it? I did not think this through. I promise, though, that it’ll work out better on subjects who don’t have slits for their pupils.