We surprised my father-in-law with the Veteran of the Day in December 2007. Because it was over the Christmas Holiday, we reserved the spot back in November. Regardless, they also chose another woman out of the crowd to participate (which we were a little disappointed because we had reserved so early). You check in about 15 minutes before the flag ceremony, at which time they tell you what to do during the ceremony. If this will be a surprise, this is the time they will "chosen" to participate, and yes, my father-in-law did tear up.
Following the ceremony, the participant gets a certificate, a special pin, and photos taken with the American Flag. Really a truly memorable experience, and I would highly recommend it.
Follow this link for some photos of our experience:
http://picasaweb.google.com/stephenlcase/DisneyChristmas2007#5149165371528005506
Hit the right arrow on you keyboard to scroll through the photos. Yes, if you keep scrolling, you will see other pictures from our trip.