Note: We're posting this in both the top level Iguazu Falls forum and the full moon-specific forum in the hope that curious travelers find it!
Last night we took the full moon tour at Iguazu falls from the Sheraton hotel. We found that getting the exact story on how that works was a little difficult, so here's how it works (at least as of last night!):
Make your reservation with the park. You can do it online before you come (as we did) or they'll happily do it from the hotel (I think without charge, but again, we didn't do it so they may try to charge you). At this point, with the reservation, you have a slot, but you should not have had to pay anything yet. The important thing to realize is that this reservation is with the park, not with the hotel. The tour is run by the park, and as such begins from the front gate of the park. Therefore, you need to pay a taxi driver to bring you there and then to pick you up to and from the Sheraton. The cost last night was $120 pesos (total, for both to and from).
One other thing to note is that when you make the reservation with the park, there is an option to get dinner with it at the park's restaurant. I would recommend doing that. This is because while the Sheraton website (and in-hotel menu book) says that the restaurant is open until 11:30, it in fact closes at 11:00. We went on the earliest tour expressly so that we could eat at the Sheraton restaurant, and found that we got back too late. We instead had to eat from the bar menu, which is limited, and expensive (and disappointing since we had hoped for a nice meal). Some review on Tripadvisor said that the food was no better than a food court's, but we went into the restaurant and while it was buffet style, it all smelled good and looked fine, and in any case was much better than what we ended up with at the Sheraton bar. So that's your best bet.
Once you get the taxi driver to take you from the Sheraton to the park's main gate, things are pretty easy. You walk about three or four blocks down a lighted path manned by park employees who will direct you to a gift shop, and there you talk to two cashiers. The first takes your reservations and your payment and directs you to the second, who checks you in and crosses your name off the list. Given the walk and the check-in process, I'd recommend that you show up about 20-25 minutes before your tour time. After that, just follow the crowd and enjoy the tour! There were instructions and guidance in both English and Spanish, and the view of the falls was incredible. Some people have said that its not worth it, but we disagree forcefully. It was really spectacular, and it's not always available, so if you have the opportunity, you should seize it. Enjoy!
I hope this helps explain the process a little and that someone finds it useful.