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.


