How is the birth of a new-born child to be celebrated on the 7th day?

Answer

There is no Sunnah custom of celebrating the birth of a child. Such customs are un-Islamic. On the seventh day, it is Sunnah to have the Aqeeqah done. The Aqeeqah is only the slaughtering of two sheep/goats for a boy, or one sheep/goat and distributing the meat – one part for the poor, one part for relatives and friends and one part for oneself. Whilst this form of distribution is Sunnah, it is permissible to distribute the meat in any way and amount as one wishes.

Whilst giving gifts is permissible, it is not an Islamic practice to make gifts on the seventh day which people have baselessly made a day of birth celebration. If you wish to give a gift, do so on any other day.