Following are the sayings that are related to birth and indicate the duties of parents to the newborn child.
Saying of Azaan 
in the ear of
a new-born child
Aboo Raafi' radhiyallahu anhu
, the freed slave of the Apostle of Allah sallallahu alayhi wasallam 
relates:
"I saw the Apostle
of Allah sallallahu alayhi
wasallam saying the Azaan of Salaat
in the ear of (his maternal
grandson), Hasan Ibne Ali radhiyallahu anhumaa
, when the child was born to (his daughter) Faatimah radhiyallahu
anhaa
."
Tirmizi, Aboo Daawood
Commentary:
In it, only the chanting of Azaan in the ear of Hasan radhiyallahu anhu is mentioned, but in another Tradition
quoted in Musnad-e-Aboo Ya'alaa Moosali, on the authority of Husayn Ibne Ali radhiyallahu
anhumaa, and
reproduced in Kanz-ul-Ummaal,
it is told that the Holy Prophet sallallahu
alayhi wasallam prescribed the saying of Azaan in the right ear and Iqaamah
in the left ear (of the new-born child), and also,
explained its propituousness. He said that, on account of it, the child remained safe from infantile epilepsy.
As these Traditions go to show, the primary claim of a
child on his family was that his ears, and through the ears, his
head and heart were made acquainted with the name of Allah
, and with His Oneness and the call of Imaan and Salaat. The best way to it, evidently,
is that Azaan and Iqaamah were said in its ears, as these impart
the knowledge of the spirit and fundamental tenets
of Islaam in a most effective manner.
The Holy Prophet sallallahu alayhi
wasallam has enjoined the saying
of Azaan and Iqaamah in the ears of a Muslim child, at the time of its birth, and the offering of Salaat-ul-Janaazah
when a
Muslim dies and his body has been bathed and covered with a shroud and made ready for the burial. He has, thus,
stressed that the life of a Muslim begins with Azaan and ends with Salaat, and ought to be spent in the way it is done while waiting and preparing for Salaat after the Azaan has been given. Besides, the fore- most claim of a
Muslim is that Azaan is said in his ears at the time of his birth and the last is
that Salaat-ul-Janaazah is offered
over him when he passes away.