Ayisha (R) reported that " whenever Prophet(SAW) was brought a newborn baby that had been born in Islam he used to say: "
اَللّٰهُمَّ اجْعَلْهُ بَارًّا تَقِيًّا رَشِيْدًا وَأَنْبِتْهُ فِي الْإِسْلَامِ نَبَاتًا حَسَنًا
Allahummaj’alhu Barran Taqiyyar Rashida, Wa Ambithu Fil Islami Nabatan Hasana
‘O Allah, make him a dutiful, righteous and rightly guided individual and grant him a wonderful upbringing in [the din of] Islam. (Musannaf Ibn Abi Shaybah)
Dua for the protection of the baby
أُعيـذُكُمـا بِكَلِـماتِ اللهِ التّـامَّة، مِنْ كُلِّ شَيْـطانٍ وَهـامَّة، وَمِنْ كُـلِّ عَـيْنٍ لامَّـة
U'eethukumaa bikalimaatil-laahit-taammati min kulli shaytaanin wa haammatin, wa min kulli 'aynin laammatin
I seek protection for the baby in the Perfect Words of Allah from every devil and every beast, and from every envious blameworthy eye.
Abu Dawud: 4737
It is narrated that when Hazrat Hussain Radiallah Tala Anhu was born, Prophet (SAW) read the Adhan in his ear and He put his own blessed Luab (Saliva) in the mouth of Hazrat Hussain Radiallah Tala Anhu and made Dua for him. (Khutbate Muharram by Faqihe Millat Mufti Jalalud Deen Ahmad Amjadi.)
How to welcome a New Born Baby
The baby should be given a ghusl immediately after birth and the umbilical cord should be cut immediately.
Azan for a new born baby:
The zikr of Allah (SWT) should be heard when the newborn baby arrives in this world. After the baby is born the Adhan should be recited in the right ear and Iqamah should be recited in the left ear by anyone who is able to recite the adhan of the salah such as the father. This should be done as soon as possible. Instructions: 1) The Muazzin (the one who recites Adhan ) should face the Qibla. 2) Place the new born baby in front of Muazzin in a way that the RIGHT ear faces him. 3) Muazzin recite the Adhan which is said for the daily salat. 4) Now place the new born baby in front of Muazzin in a way that the LEFT ear faces him. 5) This time Muazzin recite the Iqama .
Give the first sweet (Gurti) to the newborn baby:
It is stated in Tafseere Roohul Bayan that the first one giving the sweet to the baby has a certain effect on the baby that the baby develops habits similar to his/hers. It is Sunnah to have the Tahneek of the baby. Tahneek is when a Salih and Pious person bites or chews on Khurma (Date) and gives it to the baby so that the first nourishment that reaches the baby is Khurma and from the mouth of a Salih person. The Sahabae Ikram would get Tahneek of their babyren done by Rasulullah (Sallallahu alaihi wasallam)