A marker may be put on the grave any time from the end of shiva up to 12 months after death. The unveiling ceremony may occur any time between the end of sh’loshim and the first Yahrzeit. Usually, an unveiling is done about 11 months after the death.
Before the ceremony, the installed marker is covered. Psalms may be recited and someone may say a few words about the person who has died. Toward the end of the ceremony, the covering is removed from the marker and Kaddish is recited by the mourners.
Often, the unveiling is the end of the formal mourning period. The ceremony is typically short, involving only close family members and friends. It is not a requirement in Judaism, but is a tradition in this country.
For your convenience, download a copy of the Unveiling Prayer Book here