Buying Tickets for The Last Supper
The debut of the Da Vinci Code movie brought out the conspiracy seekers in droves. Only 20-25 people can see the work at one time, for a maximum of 15 minutes. Only if people don't show up will you be able to stand in line and hope to get a ticket. Tickets can be booked two months in advance but sell out quickly. Visitors must be dressed in appropriate attire for entering a church.
Last Supper tickets can be ordered online from Select Italy. Available dates and times are shown so you can choose one that fits your schedule and get a guaranteed ticket. If you don't find a date and time that is good for you, there is an option to place a request and Select Italy will try to find tickets for you.
Milan Museum sells guided tours and tickets to Milan's Museums, including the Last Supper.
Another company, Last Supper Tickets, makes some last minute tickets available for purchase a few days ahead. There's a large booking fee but the price includes English commentary during your visit. If you're looking for last minute tickets, check their site for available dates and times.
If you have a hotel already, you might try contacting them to see if they can get tickets for you.
Note: Cenacolo Vinciano is no longer selling tickets online.