I am not sure where I got this tip - either from one of the books that I borrowed last minute from the library before leaving for Milan or it was on VT. Anyways, I hope this tip is helpful to anybody who goes to Milan and wants to see Leonardo's Last Supper.
Entry to the convent next to the church of Santa Maria delle Grazie costs 6.5 Euros plus a booking fee of 1 Euro. Tickets need to be purchased much in advance. However, if you are in Milan for a very short stay, there is another alternative - expensive nonetheless.
You should book a half day tour at the Tourist Office (next to the Duomo) - I've included a picture of the tourist office here, so it should be easy for you to to locate it. The 1/2 day tour itself costs 46 Euros, but its well worth it. You get a guaranteed visit to the painting, plus you also see the Brera art gallery etc. The guides too are quite professional and give very good explanation of the sights.
My guide explained the Last Supper in quite a dramatic fashion and I don't think I will ever forget that.
We arrived at Milan's Malpensa airport. We stayed at the Principe di Savoie - a great hotel! We had a buffet lunch there at the hotel, and then set out on foot with our map in hand. We toured the Duomo and walked around the piazza and the Galleria. We went down the fancy shopping streets. Everything is fairly close together except for The Last Supper, which we walked to, and when we finally got to there, we had to buy a ticket for a viewing about 2 hours later. So we left and had to come back. Next time, we'll buy tickets for the Last Supper in advance, for an early viewing, so we can take a taxi there, and then walk back to the Duomo/Galleria area, where we'll spend most of our time.
Fondest memory: I loved the Duomo and the Galleria.
The Last Supper, the Last Pieta at the Sforza Castle, the Brera Museum for renaissance art as good as Venice's Academia or the Uffizi in Florence. Also, take the elevator to the roof of the Duomo. Easter Eve there was special.
Fondest memory: Walking around on the roof of the Duomo on a sunny day and having dinner in the canal area south of the city center.
walk through the Piazza del Duomo. You'll find there three of the most important monuments in town: the Cathedral, the Galleries Vittorio Emanuele II which connects to the Teatro alla Scala.
Fondest memory: Probably it's the painting 'Il Cenacolo' (1495-1497) painted by Leonardo Da Vinci and located at the church of Santa Maria delle Grazie. Maybe you'll find a long queue but it is well worth. Also it is interesting how the painting is being conserved and protected with a doors system which allows only a few visitors seeing the painting at the same time. Please remember that pictures cannot be made in order to preserve the painting.