When someone has died, we turn to the Lord in prayer to both give thanks for their life and to grieve. The usual process would be for the family to contact the Funeral Home. They will then be in touch with the Church to set up a date and time for the Funeral Mass.
The normal pattern for a funeral includes the following:
1. Prayers at the funeral home
2. The Funeral Mass (with the body)
3. Prayers at the cemetery and burial
This video displayed here explains the purpose of the Catholic Funeral.