One of the key features of the service I provide is the "Service" itself, also known as the ceremony.
While there isn't a canned speech, or a re-used script, simply because the ceremony is straightforward, it often enough comes out rather similar from family to family.
However, as every family is different, and as family dynamics are often different, the challenge is to find the balance that works for the particular blend of people gathered for each celebration.
We begin with a definition of terms. In this case BRIS MILAH.
People may find themselves saying "I am going to a bris" or "I went to a bris."
The truth is that you can't GO to a BRIS. A "Bris" (ברית) is a Covenant, which in this case refers specifically to the Covenant described in Genesis (בראשית) chapter 17 between God and Abraham.
MILAH (מילה) means circumcision. This is why my job is a Mohel (מוהל), circumciser, and why someone who is circumcised is described as being Mahul (מהול), and why the verb is Mal (מל) or LaMul (למול).
BRIS MILAH therefore means "The Covenant of Circumcision," which refers to the second covenant God made with Abraham, in which God made a number of promises to Abraham and his descendants, and asked that the males of Abraham's family and household bear the mark of the covenant through circumcision.
So, next time you find yourself at this kind of event, remember to throw in the word "ceremony." "I am going to a bris ceremony" (If you want to be specific about which covenant, because there are others, you should say a "bris milah ceremony") or "I attended a bris ceremony today."
Technically you were present at a Milah (circumcision), because that in fact took place. The Covenant has been around a long time, it is not being renewed at each ceremony. What we are doing is affirming our place in the covenant, and continuing the thousands-of-years tradition of bearing the mark of the Covenant in the flesh of our males.
Defining Terms Series
Bris (similar to Bris Milah)