How was circumcision practiced in Jesus' time? 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?
I got some interesting discussion in the comments when I asked this question at Mi Yodeya.  

The comments reflect various thoughts on whether it would have been practiced the same in Jesus' time as compared to today, according to the Jewish law (halacha), and why it matters (or doesn't).  There were also some incomplete answers in the comments, such as quotes of prayers or blessings that might be said and indications of who is qualified to perform the circumcision.

There was a link for an informative article about how circumcision is practiced today.  I accepted the answer at Mi Yodeya.  You can view it at this link:

https://judaism.stackexchange.com/questions/86533/how-was-brit-milah-practiced-during-the-first-century