Baby boy's mother begins the ceremony by handing her son to the Kvatterin, a woman, who assists her in introducing her son to the big occasion.  The Kvatterin then hand the baby to the Kvatter, a man (often the husband or betrothed of the Kvatterin) who assists the father in beginning the bris ceremony.  The Kvatter carries the baby to the location where the ritual of Brit Milah is performed

When the baby boy is brought into the room, the guests say  "Baruch Haba-ah," welcome! The Mohel then quotes a number of passages from the Torah in regards to the significance of the ceremony.

The Kvatter places the baby in the arms of the honored man who place the baby gently on the chair of Eliyahu Hanavi, or the chair of Elijah the prophet, and at that time the Mohel recites passages relating to Eliyahu Hanavi and his significance to the bris ceremony.

Following this, the baby is picked up from the chair of Eliyahu and presented to the father of the baby, who then hands his son over to the Sandek, the man who holds the baby during the performance of the Brit Milah ritual.

The father, who's responsibility is to bring his baby into the covenant of Abraha, appoints the Mohel as his agent to perform the Brit Milah on his son.

The Mohel recites the blessing of circumcision, and perform the brit, and the father recites the following:

Baruch ata Ado-nai, Elo-hainu Melech ha-olam,asher kidishanu, b'mitzvotav v'tzivanu l'hachniso biv-rito,shel Avraham Avinu.

Blessed are You, Lord our God, King of the universe who has sanctified us with His commandments and commanded us to bring hime into the covenant of our father Abraham.

Following the blessing, baby is handed over to the Sandek Shainy  (second sandek) who holds the baby during the naming ceremony.  Once baby is named, Kvatter brings the newly circumcised baby back to his mother's arms.

A "Seudat Mitzvah," a meal in honor of observing the mitzvah (commandment) commences then,  with the blessing over the Challah (Ceremonial Bread).  At the conclusion of the festive meal, one of the male participants is honored to lead in the rest of the party with "Birkat Hamazon," Grace after Meal blessings, and six people recite special blessings for the family and honorees of the Brit Milah ceremony.
 

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More about the Brit Milah:
• Brit Milah: The Covenant of Circumcision, an overview.
• Brit Milah: Biblical Commandment
• Leil Shimurim: The Evening Before the Brit Ceremony
• Brit Milah: The Venue
• Brit Milah: Best time for Ceremony
• Brit Milah: The Ceremony
• Brit Milah: The Controversy
       • Brit Milah: Benefits - AP Article
       • Brit Milah: Benefits - BBC Article

• Jewish Baby Names from A to Z