Abu Dawud

Benefits and Issues:
➊
The livelihood of the Messenger of Allah (sallallahu alayhi wa sallam) was limited to subsistence and contentment.
Whatever he had, he would generally give in charity, yet despite this, he (sallallahu alayhi wa sallam) would make arrangements for sacrifice (udhiyah).
Similarly, he would also keep weapons ready for jihad.

➋
On the occasion of sacrifice, it is legislated and required to sacrifice an animal rather than giving money in charity.
Giving the price of the animal as charity can never be a substitute for sacrifice.

➌
A camel is slaughtered by nahr.
That is, a knife is thrust into the soft part at the base of the neck near the collarbone.
The method of slaughtering a camel according to the Qur’an and Sunnah is that it should be slaughtered while standing.
The statement of Allah, the Exalted, is:
(And the camels and cattle We have appointed for you as among the symbols of Allah; for you therein is good. So mention the name of Allah upon them when lined up [for sacrifice].) (: Al-Hajj 36)
And the sacrificial camels, We have made them for you among the symbols of Allah.
There is good for you in them.
Therefore, (at the time of nahr) when they are standing with their legs bound, mention the name of Allah over them.
Ibn Abbas (radi Allahu anhu) says in the explanation of “sawaaf” that it means (standing).
That is, the camel should be slaughtered (nahr) while it is standing.
(Sahih al-Bukhari, Book of Hajj, Chapter: Slaughtering the Camel While Standing)
In addition, the camel’s left leg should be tied.
The Noble Prophet (sallallahu alayhi wa sallam) and the Companions (radi Allahu anhum ajma’in) used to slaughter the camel in this manner.
Jabir (radi Allahu anhu) narrates that the Noble Prophet (sallallahu alayhi wa sallam) and the Companions (radi Allahu anhum ajma’in) would slaughter the camel in this state:
the left leg would be tied, and it would be standing on the remaining three legs.
(Sunan Abi Dawud, Book of Manasik, Chapter: How to Slaughter the Camel, Hadith 1767)
Ziyad bin Jubair (radi Allahu anhu) narrates:
I saw Ibn Umar (radi Allahu anhu) come to a man who had made his she-camel sit down for slaughter.
He (Ibn Umar) said: Make it stand and tie it.
This is the Sunnah of Muhammad, the Messenger of Allah (sallallahu alayhi wa sallam).
(Sahih al-Bukhari, Book of Hajj, Chapter: Slaughtering the Camel While Standing, Hadith 1713)
Other than camels, other animals are slaughtered (dhabh).
That is, their throat and the accompanying veins are cut.

Hadith Commentary:
The purpose of the chapter is that the Noble Prophet (sallallahu alayhi wa sallam) himself slaughtered the camels with his own hand; thus, the heading of the chapter is established.

Hadith Commentary:
(1)
Imam Bukhari rahimahullah has narrated this hadith in a concise manner; later on, he himself will narrate it in detail.
(Sahih al-Bukhari, al-Hajj, Hadith: 1714)
In this hadith, it is explicitly stated that the Messenger of Allah sallallahu alayhi wa sallam sacrificed the camels for offering with his own blessed hand.

(2)
In this hadith, Anas radi Allahu anhu has described his own observation.
In Sahih Muslim, there is a lengthy hadith narrated from Jabir radi Allahu anhu, in which he states that the Messenger of Allah sallallahu alayhi wa sallam slaughtered sixty-three camels with his own blessed hand, and for the remaining camels out of one hundred, he appointed Ali radi Allahu anhu to sacrifice them.
(Sahih Muslim, al-Hajj, Hadith: 2950(1218))

Benefits and Issues:
It is preferable to perform the sacrifice (qurbani) with one’s own hand, but another person may also perform the slaughter, as in the Farewell Pilgrimage (Hajjat al-Wada‘) when the Messenger of Allah (sallallahu alayhi wa sallam) offered the sacrifice on behalf of his noble wives (radi Allahu anhunna). They only came to know of it when the meat reached them. (See Hadith: 2981)

Takhrij:
«أخرجه البخاري، الحج، باب من نحر هدية بيده، حديث:1712، حديث:5553، 5558 وغيره، وحديث عائشة: أخرجه مسلم، الأضاحي، حديث:1967.»©Explanation:
➊ The Messenger of Allah (sallallahu alayhi wa sallam) preferred to offer sacrifice of a large, well-built animal.
➋ Before sacrificing, the knife should be thoroughly sharpened.
➌ The animal should be laid down on its side for slaughter.
➍ Before slaughtering, the prescribed supplication (dua) and the takbir should be recited.
Apart from the supplication mentioned in the above hadith, another supplication is also established to be recited at the time of slaughter.
And that supplication is: «إِنِّي وَجَّھْتُ وَجْھِيَ لِلَّذِي فَطَرَ السَّمٰوٰتِ وَاْلأَرضَ عَلٰی مِلَّۃِ إِبْرَاھِیمَ حَنِیفًا وَّمَا أَنَا مِنَ الْمُشْرِکِینَ‘ إِنَّ صَلاَتِي وَ نُسُکِي وَ مَحْیَايَ وَ مَمَاتِي لِلّٰہِ رَبِّ الْعَالَمِینَ‘ لاَ شَرِیکَ لَہُ وَبِذٰلِکَ أُمِرْتُ وَ أَنَا مِنَ الْمُسْلِمِینَ‘ اَللّٰھُمَّ! مِنْکَ وَلَکَ عَنْ مُحَمَّدٍ وَّ أُمَّتِہِ بِسْمِ اللّٰہِ وَ اللّٰہُ أَکْبَرُ» (Musnad Ahmad: 3/375; Sunan Abi Dawud, Kitab al-Dahaya, Chapter: What is recommended regarding sacrificial animals, Hadith: 2795). In the supplication, instead of the words: «عَنْ مُحَمَّدٍ وَ أُمَّتِہِ», one should mention one's own name, the names of one's family members, or the name of the person on whose behalf the sacrifice is being made.
➎ By sacrificing one animal on behalf of the household, the Sunnah is fulfilled.
➏ One should perform the sacrifice with one's own hand, although deputizing someone else is also permissible.
➐ Performing sacrifice on behalf of a deceased person is not established by any authentic hadith.
It is not correct to deduce this from the general practice of the Messenger of Allah (sallallahu alayhi wa sallam), because according to some scholars, this was a specific characteristic of the Prophet, in which following him is not permissible for the Ummah.
See: (Irwa’ al-Ghalil: 4/354). Furthermore, even in the best generations (the eras of the Companions and the Followers), there is no evidence of sacrificing on behalf of the deceased.
It can only be considered permissible from one perspective: that giving charity on behalf of the deceased is allowed, i.e., as a means of conveying reward (isal al-thawab), its denial is not possible.
And Allah knows best.
For further details, see: (Sunan Abi Dawud, Urdu, Darussalam edition, Benefits and Issues of Hadith: 2790).