I am a bigger red eye nazis than I realized. I had to go all the way back to pictures from my DAD's mission to find a suitable picture.
Find your picture using Picasa. Go Here to download it for free. Click on it and make it bigger. On the Basic Fixes pallet which is the first one that opens when you make the image bigger, select the red eye button. It is the top right one.
Picasa will then auto correct any red eye it finds. Your job is to make sure it corrected all of the right things.
It will highlight green all of the places it thinks need to be red eye corrected. Sometimes it cannot find the red eye and you will have to drag a little box around the eye. Just click on the eye and then drag and a little white box will appear as it did with the guy in the center of this picture.
As with this fellow, sometimes Picasa selects too much. All you have to do is bring your mouse to rest over the green boxes you don't like and I little white X will appear. Click that X on the green boxes that shouldn't be there.
Hit apply and you have no more redeye.
To finish your red eye fix, you need to return to your library and select the Save to Disk option in the top right hand corner. This will save over your originals. Saving over your originals is bad when you want to keep the original but if you have just improved by fixing the red eye you probably just want the improved version.