Recommended Actions of Slaughtering Al-Udhiyah:

It is permissible for the Muslim to slaughter an Udhiyah for himself, on behalf of his household (the ones who live with him in the same house) and on behalf of those on whom he spends, and all of them will share the reward with him. 

One of the recommended actions the owner of Al-Udhiyah should perform is to face Al-Qiblah while slaughtering it, to perform the slaughtering himself if he can and to say before slaughtering Al-Udhiyah the following:     

(Bismillah wa Allahu Akbar: (In the Name of Allah; Allah is the Greatest). O Allah it comes from You, and it is given to You. O Allah accept it from me and from my household) 

He can ask someone else to slaughter his own Udhiyah, but he should witness that as the Prophet, peace be upon him, instructed Fatimah, may Allah be pleased with her in the following Hadith: 

(Ali (may Allah be pleased with him) narrated that the Messenger of Allah (peace be upon him) said, "O Fatimah! Come and witness your sacrificial animal (being slaughtered), for surely, by its first drop of blood that falls on the ground, all your sins are forgiven.")

It is desirable to divide Al-Udhiyah into three equal parts; one third is for the owner of the Udhiyah and for his household to be eaten, the other third is dedicated to his relatives, friends and neighbours and the last third is given to the poor and needy Muslims as Allah the Almighty orders us in the following Ayah:    

(...eat thereof, and feed the beggar who does not ask (men), and the beggar who asks (men).)

[Al-Hajj, 36]

Allah the Almighty says: 
 

(Whose hearts are filled with fear when Allah is mentioned; who patiently bear whatever may befall them (of calamities); and who perform As-Salat (Iqamat-as-Salat), and who spend (in Allah's Cause) out of what We have provided them* And the Budn (cows, oxen, or camels driven to be offered as sacrifices by the pilgrims at the sanctuary of Makkah.) We have made for you as among the Symbols of Allah, therein you have much good. So mention the Name of Allah over them when they are drawn up in lines (for sacrifice). Then, when they are down on their sides (after slaughter), eat thereof, and feed the beggar who does not ask (men), and the beggar who asks (men). Thus have We made them subject to you that you may be grateful* It is neither their meat nor their blood that reaches Allah, but it is piety from you that reaches Him. Thus have We made them subject to you that you may magnify Allah for His Guidance to you. And give glad tidings (O Muhammad PBUH) to the Muhsinun (doers of good).)

[Al-Hajj, 35-37]