Christening (baptizing) a baby was the important first stage of medieval life. If the baby looked sickly, it was done immediately, in case the infant died. For a healthy baby, the ceremony waited a week, but was usually done within six weeks, during the period when the mother was resting and not permitted to come to church. Parents were spectators, if the mother was there at all.
In the ceremony, friends presented the baby for baptism; they were known in English as “godparents.” Eventually, custom dictated that a baby boy needed two men and a woman as godparents, while a baby girl had two women and one man. They could not be relatives within any close degree, and families had to choose carefully because the Church considered godparents to be relatives to that infant. When grown, the child could not marry into the godparent’s family. It worked best if couples became godparents for each others’ children, and since being a godparents was an honor, people often went by work-related ties, like guild members standing up for each others’ babies.
Medieval infants were baptized by immersion; they were immersed quickly three times in a ceremonial container of water, the baptismal font. Then the priest drew a cross on the infant’s forehead with holy oil and they wrapped the baby in a white hooded robe that covered head and forehead, in theory preserving the holy oil for as long as possible.
Godparents usually gave the infant a gold coin as a christening gift. Whatever future relationship they had to the child (in some cases close and familial, in others distant and merely honorary), they made the first deposit for the baby’s life savings.
Edit: July 2024
Jewish infants in medieval Europe were circumcised, as they had always been. This ceremony probably took place at home, but at least the naming ceremony portion was held at the synagogue. There was a celebratory feast, which took place at home, but sometimes in a Jewish community center. Like the Christian godparents who presented the baby for baptism, the Jewish baby boy was held by a “pious and learned man, not necessarily a relative,” who was expected to play an ongoing role in the boy’s life.
There’s one distinctive detail about medieval Jews: in some communities including Germany, they believed that Adam’s first wife, Lilith, might come to steal the child before he could be circumcised. Therefore the adults held a “Watch Night” on the eve of the circumcision, probably in the family’s house.
(Details about Jewish infants are from The Jews in the Middle Ages, by Norman Roth (Greenwood Press, 2005), p. 112)