Both John the Baptist and Jesus were circumcised on the 8th day, according to Old Testament laws.
Luke 1:57-60 English Standard Version (ESV)
Now the time came for Elizabeth to give birth, and she bore a son. And her neighbors and relatives heard that the Lord had shown great mercy to her, and they rejoiced with her. And on the eighth day they came to circumcise the child. And they would have called him Zechariah after his father, but his mother answered, “No; he shall be called John.”
Luke 2:21-39 English Standard Version (ESV)
And at the end of eight days, when he was circumcised, he was called Jesus, the name given by the angel before he was conceived in the womb.
Did a priest come to the home to perform the circumcision? Were there formal traditions or prayers recited, and if so, what do we know about them and how do we know about them?