The Archdiocese of Turin's Shroud site gives the cathedral's hours as every day from 9:00 a.m. to 12:30 p.m. and from 3:00 to 7:00 p.m., and the tomb is visited in those hours. It is a side chapel in a working cathedral, so expect a place of quiet prayer and not a museum display. If Mass is being celebrated when you arrive, wait until it has ended before walking up the aisle.
Frassati was born in Turin in 1901 and died there on July 4, 1925, at the age of 24; July 4 is his feast day. He was an engineering student and a Dominican tertiary, and he is widely invoked by students, young people and mountaineers.
Good to know before you go: the chapel where the Shroud is kept is at the end of the same left aisle, so one visit takes in both, although the Shroud itself stays sealed in its case and cannot be seen. Pilgrims who give Turin a full day often add the Museum of the Shroud, about ten minutes' walk from the cathedral, and Don Bosco's tomb in the Basilica of Mary Help of Christians at Valdocco.