Tickets to view Leonardo Da Vinci's Last Supper are frequently sold out weeks in advance. As of Oct 2009, the reservation service has been awarded to Vivaticket, a ticket agency: http://www.vivaticket.it/evento.php?i.... Reservations can be made on line or by telephone. Operators speak English.
Other options involve visiting The Last Supper (ticket included) as part of a tour. These are far more expensive than the official avenues, but worth it if you don't want to miss out. See http://www.tripadvisor.com/Travel-g18...
There are also ticket re-sellers (such as Tickitaly and others), but of course in this case tickets will be heavily marked up.
The last -- and most expensive -- option could be a private guide service (such as Milan Guide Services), who will be friendly, helpful and available on the date required, albeit at a cost of €120 for a 1hr guided tour.