There are many traditions and customs practiced in our community and in most Sephardic communities at the time of the Berit Milah.
The father of the baby and the Sandak (the person honored to hold the baby as, the Mohel performs the circumcision), both wear a Talit for the ceremony.
After the Berit, all guests are welcome to come to the Sandak and receive a personal blessing from him. The Sandak should prepare himself for this special moment, bearing the merit and responsibly involved in blessing properly each individual.
The family of the baby brings red apples and distributes them among the male guests, after the Berit.
Some families in our community have the custom to do the Berit Itzchak, the night before the Berit Mila. This ceremony takes place after Arbit. In preparation for the Berit Mila the attendees read some texts from the Torah, the Talmud and excerpts from the Zohar. These texts refer to the importance of the Berit Milah, beginning of course, with Abraham Abinu. At the end of the ceremony, the attendees bless the baby and wish him and his family HaShem's blessings.
In some Ashkenazi communities, the night before the circumcision, young children come to the home of the newborn baby and recite Torah verses. This ceremony is called vacht nacht in Yiddish, "night of watching.
The morning of the Berit, the father should make every effort to attend services (Shacharit) before the Berit.
Our community custom is that, when somebody in the community has a Berit Mila, even if he himself is not present there, we skip the recitation of ANA (Viduy-confession) in all of the community Minyanim (for Shacharit only!).