I know much of this has been posted before, but since I just checked on Last Supper Tickets, I thought I'd share what I learned:
Many people have posted that it's necessary to reserve Last Supper tickets many months in advance. I just tried to book for next summer, and found that tickets are only available three months ahead of time. So if you book today, the only dates that show are from this week through February 28.
By the way, the official website is www.cenacolovinciano.net. I checked a couple of tour sites, as well, and they didn't have tickets available yet, either.
So I guess we should start checking the website about 4 months out, and keep right on it.
Oh, there are still quite a few days open this month, but only one day available in February. Although according to Rick's Italy book, you might have better luck over the phone, because the available dates on the website don't reflect cancellations. The phone number is (from the US) 011-39-02-9280-0360; then press 2 for English.