The three days from August 13th through 15th is called "Bon." In Buddhism it is believed that dead people's spirits come back to their family during these three days. Although few Japanese are very religious, "Bon" is an important annual event to many. They (or "We", because I am also one of them) set up some rituals to welcome the spirits of their dead family members. They differ from region to region. I will tell you what is usually done in my region.
The first thing is to prepare a special lantern. It usually has each family's crest, the sign of the family, on it. We are told that the lantern is necessary for a spirit to find his or her house because they can only see the light from the lantern.
The second thing to do is light torches at the front door. On the evening of August 13, every family member comes together in front of the door to light them. It is a ritual to call the spirits over to the family. I don't believe in the coming of the spirits, but I like this because, when I watch the torches burn, I feel serene and memories of the dead people come back to my mind.
"Bon" makes us more religious than usual. All the family members go to their family grave, give it flowers, and light incense sticks for praying. At home, sweet rice cake coated with reddish beans is placed on the altar as an offering. Many families have priests come to their houses to hold a Buddhist service.
After staying with us, the spirits of the dead are said to leave on the evening of August 15th. We again light torches to see them off. It makes us a little sentimental.