My understanding is circumcision should be performed on the eighth day. Does this include the day the child was born? So if born on Monday, would circumcision be on the following Monday, or should it be 1 week + 1 day (Tuesday)?
The day of the birth is included in counting towards the eighth day of life:
A Brit Milah should be performed on the infant's eighth day (including the day of birth), after sunrise. If the circumcision was performed before sunrise on the eighth day, it is nevertheless valid, so long as it took place after daybreak.
(from http://www.dailyhalacha.com/displayRead.asp?readID=1228 Rabbi Eli Mansour)
Breishit 17:12 uses the phrase בן שמונת ימים which (loosely) means "an 8-day old".
When the Torah uses the phrase בן followed by a number to refer to someone's age, it is counted from the date of birth, or the first day of a person's life.
What, perhaps, may confuse the count is if a child is born during twilight. In such situations, you may need to check with a rav to verify exactly what the Hebrew date of birth is to know when the 8th day is.