Avraham was commanded to circumcise himself and all males in his household. From then on, all healthy Jewish males were to be circumcised when they reached 8 days old.
If there is any question about the baby's health, the circumcision is delayed or, in rare cases, not done at all.
The primary obligation to do the circumcision is on the boy's father. Since most people are not skilled surgeons, the actual cutting is usually done by a highly trained expert, called a mohel, who is appointed by the father. A festive meal is eaten after the circumcision.  A minyan is preferred, but not required, for a brit mila.
 

For a boy who requires an operation six months later (or more) to repair an anomalous condition such as hypospadias or webbing--if the hospital will allow a mohel "hands-on" participation, then the brit mila is done at the time of the operation. 
If not, after the child heals, a hatafat dam brit mila should be performed.

A father should circumcise his male children (if he knows how to do to the circumcision!) or appoint someone to do so. Order of preference for who should do the circumcision, if competent:

• Father
• Other shomer-Shabbat male
• Shomer-Shabbat woman (if no male is available).

Choose the greatest Jewish scholar (talmid chacham) in your town or city as sandak (person who holds the baby for the brit mila), since kabbala says it is a good omen for the boy's soul. A woman may be a sandeket but only if no suitable man is available.  If no Jewish man or woman is available, a non-Jewish person may serve as a sandak or sandeket.

When doing a circumcision, metzitza (sucking out some blood) is required.  Metzitza may be done using a pipette or other tube, but the traditional way is by mouth.

There is no minimum amount of blood to draw out for metzitza: any quantity suffices.
 

Don't formally invite people to a brit mila meal, just announce it.
Reason If you invite people and they don't come, they are disrespecting the chance to participate in a mitzva.  

You are not halachically required to name the baby after a particular person. The custom is that a baby is not named after its living parent.

A se'udat mitzva is required for a brit mila, but the brit mila is still valid even if no meal is held. The minimum requirement for the meal is to eat at least 1.3 fl. oz. (39 ml, or 1/6 cup) of bread within four minutes.

If a brit mila is performed on Tish'a b'Av or other fast days, the meal (se'udat mitzva) is held after the fast ends. On a delayed fast day, the sandak, mohel, and father of the boy who is having the brit may eat after mincha.