The famous Last Supper fresco of Leonardo da Vinci is situated in the refectory of the Santa Maria delle Grazie church, which you'll find along the Corso Magenta. It miraculously survived the WWII devastations and underwent a 20 year restoration that was completed in 1999.
The only way visitors to Milan can see this masterwork without advance reservations is to book a guided tour.
Take for example the three-hour Autostradale bus tour or the ATM City tour.
The Autostradale tour (55 euro, credit cards accepted, not on Monday) departs from Piazza del Duomo in front of the Cathedral, near Mac Donald's, at 9.30 am, lasts three hours and includes Cathedral - Gallery - Scala - Sforza Castle - Last Supper - Arch of Peace - Arena - Monumental Cemetery. Price includes transport from and to main hotels, entrance fees to monuments and guided tour. On-line booking from the Autostradale website.
The ATM tour costs 60 euro and operates from Tuesday to Sunday, from 9:30 a.m. in Largo Cairoli (opposite the Castello) and ends at about 1:00 in Piazza Duomo. The website gives a schedule. Info line 02 48036999. There are also tours, albeit with a slightly different program, but including the Last Supper, on Wednesdays (1 pm) and Friday/Saturday (2.15 pm).
On the Internet you may find other tours at different costs, e.g. at 24Milano and Zani Viaggi, Viator, and TicketItaly.
Yet another possibility is to book at least a few days in advance with LastSupperTickets, 29 euro.
To pay the normal entrance fee of 6.50 euro you'll have to make a reservation the official way, at the Vivaticket website, months in advance! Be alert as the availability of tickets changes rather a lot over time, so come back to the site regularly (you may just have luck).
On site there are guided English language tours at 9.30 and 3.30 (3.50 euro extra fee). To book this guided tour, you first need to get tickets for one of the two periods and then contact the call center (02 92800360) to book the guide.
At the Santa Maria delle Grazie small groups are allowed in at a time and you get 15 minutes to spend in the (noisy) room, in which on the wall opposite of the last Supper fresco you may also admire a Crucifixion by Donato di Montorfano (if you have time left).
The Last Supper is accessible for the disabled (parking your car may present difficulties though).
Source: Milan & More City Guide App fro Smartphone