Which prayer is recited while sacrificing?
It is necessary to comply with some conditions while fulfilling the wajib of sacrifice, which has an important place in our religion. There are prayers to be done and prayers to be recited before and during the fulfilment of this worship.

It is beneficial for the person who sacrifices the qurbani to be ablution as much as possible. However, he should definitely slaughter with ‘Besmele’ when slaughtering. This means that the slaughtered animal is a sacrifice dedicated to Allah and the worship is dedicated to Allah.
The slaughter of the one who deliberately leaves the Besmela is haram.
It was narrated from Anas b. Malik (r.a.): ‘Rasulullah (s.a.w.) sacrificed two horned, pied coloured rams with his own hand. He said: ‘The Messenger of Allah (s.a.w) slaughtered two rams with horns and pied coloured rams with his own hand.’

The prayer to be recited while sacrificing and the slaughtering procedure are as follows.
The intention to sacrifice is as follows:
‘O Lord, I intend to sacrifice for your sake. This body of mine has committed many misdemeanours and sins. I have to sacrifice this body to you. But You have made it forbidden. I am sacrificing this sacrifice that you have favoured for my sinful, helpless body in accordance with your consent and command.’

With Besmele-i sharifa:

إِنِّي وَجَّهْتُ وَجْهِيَ لِلَّذِي فَطَرَ السَّمَاوَاتِ وَالْأَرْضَ حَنِيفًا وَمََا أَنَا مِنَ الْمُشْرِكِينَ
‘Innî wajjattu wajhiye lillezî fetara's-samâvâti wa'l-ararar hanîfen wa mâ ene mine'l- mushrikîn.’

اَللّٰهُمَّ هٰذَا مِنْكَ وَلَكَ اَللّٰهُمَّ اِنَّ صَلٰهُمَّ اِنَّ صَلٰتِى وَ نُسُكِى وَمَحْيَاىَ وَمَمَاتِى ِلللهِ رَبِّ الْعَالَمِينَ لَ شَرِيكَ لَهُ وَبِذٰلِكَ اُمِرْتُ وَاَنَا اَوَّلُ الْمُسْلِمِينَ
‘Allâhumma hâzâ minke wa lke. Allâhumma inna salâtî wa nüsükî wa mahyâya wa mamâtî lillâhi rabbi'l-âlamîn, lâ sharîke lahû wa bizâlike umirtu wa ene ana firstu'l-muslimîn.’ then:

اَللهُ اَكْبَرْ اَللهُ اَكْبَرْ اَللَا اِلٰهَ اِلَّا اللهُ وَاللهُ اَكْبَرْاَللهُ اَكْبَرْ وَ ِلللهِ الْحَمْدْ بِسْمِ اللهِ اَللهُ اَكْبَرْ
‘Allâhu akbar Allâhu akbar. Lâ ilâhe illallâhu waallâhu akbar. Allâhu akbar wa lillâhi'l hamd, Bismillâhi Allâhu akbar.’ and slaughtered immediately.

How is the sacrifice slaughtered?
The following four parts of the sacrifice are slaughtered:

The windpipe
Oesophagus
Two jugular veins
-It is sunnah to slaughter these four. (Hindiyya)
-It is permissible to slaughter three of them.
-It is sunnah to slaughter a camel by its neck while standing, sheep, goats and cattle by lying down and slaughtering them between the chin and the chest, under the bone called the nub.
-It is sunnah to slaughter the sacrificial animal by turning it towards the qibla and tying its front legs and back right leg. The camel is slaughtered standing up (Wahdatî).
-It is permissible to tie the four legs of cattle for convenience.