There are 2 things in Aqeeqah ceremony: the shaving of the hair from the head of a newborn baby, and the sacrifice of an animal (these were also characteristic features of Millat-u-Ibrahim, the religion of the Prophet Ibrahim).
The hair on the child's head is shaven and its weight in silver is given as charity. An animal is then sacrificed as a mark of celebration and distributed amongst friends, family, the poor and a portion is kept for ones own consumption.
Ali (RA) reported that the Messenger of Allah slaughtered a goat on the occasion of Hasan's birth, the son of Fatimha (RA) and Ali (RA) and said "Oh Fatimah! Shave the head of Hasan and pay silver equal to the weight of the hair as charity".
Sahih Sunan at-Tirmithee 2:1226
It is reported by Abdullah bin al-As that the Prophet said, "To whomsoever a child is born and he wants to perform a sacrifice of Aqeeqah on behalf of it, he should sacrifice two goats for a boy and one goat for a girl".
Sunan Abu Dawood 2:2836
"During the age of ignorance, when a child was born to anyone of us, we used to slaughter a goat and smear the child with its blood. Later, after the dawn of Islam, our practice became (on the advice of the Prophet) that we sacrifice a goat of Aqeeqah on the seventh day after the birth of the child, shave the head of the infant and apply saffron on it".
Sunan Abu Dawood 2:2137