The mother of the baby enters the hall with the baby. It is customary to honor relatives and friends (generally couples that are not yet parents) as 'kvaters' (carriers), who are entrusted to transfer the baby from his mother to his father. The father, the sandek (generally one of the senior men in the family), and the mohel approach the bimah (platform) where the ceremony takes place. The father wraps himself in a tallit. Then the mohel calls the 'kvaters' to transfer the baby, from his mother to his father.
In the first part of the ceremony, the father, the mohel and the congregation take turns reciting certain verses, mostly from Psalms. The mother has no official responsibilities during the brit and may prefer to stand towards the back.
The congregation and mohel recite the first prayers as the baby is brought in. The father receives the child, and recites additional verses responsively with the congregation. Then he places the child (on the pillow) on the sandek's lap (who is sitting on 'Elijah's chair'). While still reciting these prayers, the mohel removes the baby's lower garments, wraps him in a cloth diaper and prepares him for the brit. Though a baby will often cry already during this stage, in actuality this undressing and diapering is no different or more painful for him than usual.
Though the brit milah procedure is uniform, Ashkenazic, Sephardic and Yemenite traditions reflect different variations of the texts recited at the ceremony. The main tradition is offered here, in its shortest versions. Different mohels may add certain psalms, piyuts (hymns), and other prayers.
Click here for the English text of the Brit ceremony