The Jew is bound to a covenant engraved deep beyond his conscious awareness, even in his very flesh: an eternal union that God established with Abraham Avinu (our father). Long before he can be conscious of it, his mother and father bring him into this covenant through circumcision.
The Brit (Covenant) must be performed by a skilled and God-fearing Mohel (the one who performs the circumcision). A few days after birth, the Mohel examines the baby to ensure everything is ready for the circumcision. Ideally, the Brit is performed on the eighth day of life, during the day. If the baby's health requires it, it is postponed to another day.
If the child was born on Shabbat, the Brit can be performed on the following Shabbat, but if it had to be postponed, it is not planned to be performed on Shabbat.
If for some reason the Brit test was not done at eight days, it can be done later, even as an adult, with a properly trained Mohel and with local anesthesia.
The ceremony is a joyous occasion. It is customary not to invite people but only to notify them, because the prophet Elijah participates in every Brit, and it is disrespectful to him if someone is invited and does not attend.
A blessing is said, the circumcision is performed, and then the baby is given a name. Afterward, a festive meal is offered.