بسم الله الرحمن الرحيم 'In the name of God, Most Gracious, Most Merciful'
One of the best righteous deeds that you are requested to do of ten days of Zul-Hijjah is the Al-Odheya (أضحية) or Qurbani, which is the sacrifice of an animal.
Warning against leaving it: (سنة مؤكدة or Highly encouraged)
One must do an offering for sacrifice of a cattle animal (goat/sheep, cow, or camel) if you are not going for Hajj and capable of doing it.
The prophet (peace be upon him) warned against leaving it when he said "He who has the financial ability to offer sacrifice (of an animal) but he doesn't do, it is not allowed for him to come near our place of Eid prayer." (Al-Albani)
«من كان له سعة و لم يضح ، فلا يقربن مصلانا»
One sacrifice animal is sufficient on behalf of the entire family under the same roof. It is not mandatory for each individual in the household. You can slaughter more if you are wealthy and should not cause any burden on you. You can also include the ones that died and passed away in the same sacrificed animal. You don't have to say loudly the names who the sacrifice animal is intended for. What count is the intention. However, Uttering it before slaughtering the animal is just a sunnah since The prophet (peace be upon him) said "This is on behalf of my family and the Umma of Mohamed"
Preparing ourselves for it:
The prophet (peace be upon him) said "He who has a sacrificial animal with him whom (he intends) to offer as sacrifice, and he enters the month of Zul-Hijjah, he should not get his hair cut or nails trimmed until he has sacrificed the animal." (Muslim)
«إذا رأيتم هلال ذي الحجة ، وأراد أحدكم أن يضحي ، فليمسك عن شعره وأظفار» ه
The reason to abstain from cutting the hair and nails is to resemble to the people that are standing in Hajj and doing Tahrim. But if someone forgets, there is no harm.
The days of Odheya (sacrifice):
Muslim can offer his sacrifice in the day of Eid (the tenth day of Zul-Hijjah month) and the three days followed it, as the prophet (peace be upon him) said «slaughtering (of animals as a sacrifice) is permissible in all the days of Tashreeq (11th, 12th, and 13th of Zul-Hijjah)» (Al-Albani)
«كل أيام التشريق ذبح»
Notice: these days (the days of Tashreeq) were named with this name because the people of Mecca were spreading the meats of Hadi (sheep, cow, or camel) on rocks to the direction of the sun shine till it becomes dried meat that can be preserved till they need it.
The best times for Odheya:
The best time for it is directly after Eid prayer, but it is not permissible before the prayer and after the sunset of the 13th of Zul-Hijjah. Otherwise, it's not consider to be Odheya nor a Sacrifice, just a normal slaughter meat.
The prophet (peace be upon him) said "The first (act) with which we started our day (the day of Eid-Al Adha) was that we offered prayer. We then returned and sacrificed the animals and he who did that in fact adhered to our Sunnah (practice). And he who slaughtered the (animal on that day before the Eid prayer), for him (the slaughtering of animal was directed to the acquiring of) meat for his family, and there is nothing of the sort of sacrifice." [Agreed upon]
«إن أول نسكنا في يومنا هذا أن نبدأ بالصلاة ، ثم نرجع فننحر ، فمن فعل ذلك فقد وافق سنتنا ، ومن ذبح قبل ذلك فإنما هو شيء عجله لأهله ، ليس من النسك في شيء»
The act of Slaughtering Odheya:
It's better to slaughter with your own hands or if someone do it on your behalf, he must be a Muslim or someone who is Kitabi (from the people of the books)
Must say Bismillah and Allah Akbar
Make intention that this is an Odheya and this is the sacrifice for Eid
When sacrificing an animal, it must be done with Ihsan, easy, gentle, and nice way so Allah SWT will show you mercy. For example, don't slaughtering the animal in a group when animal see each others or don't sharpen the knife in front of the animal or slaughter the animal twice.
The Age limit for Odheya:
You must select something that is re-presentable to Allah SWT when offering a sacrifice. Odheya cannot be the cheapest or defective and must be free of any deficiencies, for example limping or sick animal.
Age limit for sheep is minimum 6 month
Age limit for goat is minimum 1 year
Age limit for cow is minimum 2 year
Age limit for camel is minimum 5 year
The best place for slaughtering Odheya:
The best place for slaughtering the sacrificial animal is in the place of Eid prayer if it is possible.
Ibn 'Umar said, "Allah's Apostle used to slaughter (camels and sheep, etc.,) as sacrifices at the Musalla (the place of Eid prayer)" (Al-Bukhari).
«كان رسول الله صلى الله عليه وسلم يذبح وينحر بالمصلى»
What to do with the meat of the slaughtered animal:
The prophet (peace be upon him) used not to eat on the day of Eid Al-Adha till he prayed and then came to eat of his slaughtered animal (Narrated by Imam Ahmad and declared Hasan (good) by Al-'Rna'oot).
"لا يأكل يوم الأضحى حتى يرجع فيأكل من أضحيته"
According to scholars, you must divide the meat into 3 parts to distribute:
1 part is to be given for the poor and needy as a Sadakah (charity)
2 part is to be given for relatives and neighbors as a gift. It can be given to non-Muslim and wealthy
3 part is to be consumed by you and your family
If you give a little more here and little bit less there, it is no problem inchallah.
You must own the Odheya before slaughtering it and you can't pay the person that slaughter for you from the Odheya.
Dear brothers and sisters,
you should be keen on taking this great chance (the first ten days of Zul-Hijjah), before it becomes too late, to win Allah's content.
Almighty Allah says in the Glorious Quran (Surat 3 Al-‘Imran Ayat 133).
And we ask Almighty Allah to support us to do what He likes and accept, we ask Him also to accept your righteous deeds and give you great reward.
Allah knows best الله اعلم