We have a description by Eusebius Vita Const. iv. c. 60. of some of these ceremonies in the case of Constantine:  When the Emperor felt his life to be drawing to a close, “he poured forth his supplications and confessions to God, kneeling on the pavement in the Church itself, in which he also now for the first time received the imposition of hands with prayer.”  Soon after this the Bishops whom he had summoned to Nicomedia to give him Baptism, “performed the sacred ceremonies in the usual manner, and having given him the necessary instructions made him a partaker of the mystic ordinances.”