All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness. 2 Timothy 3:16
Animal Sacrifice
The first nine chapters of Leviticfus can be summarized as follows: Get an animal, kill it, sprinkle the blood around, cut the dead animal into pieces, and burn it for a "sweet savor unto the Lord."
The phrase "sweet savour" occurs 39 times in the King James Version, when referring to the pleasure God gets from smelling the burning flesh of animal sacrifices.
The first occurrence of the phrase is when Noah sacrifices the every clean beast and fowl that he took with him on the ark (thereby causing the extinction of all clean beasts). God loved the smell of Noah's sacrifice so much that he promised never to curse the ground or kill everything living thing ever again.
And Noah builded an altar unto the LORD; and took of every clean beast, and of every clean fowl, and offered burnt offerings on the altar.
And the LORD smelled a sweet savour; and the LORD said in his heart, I will not again curse the ground any more for man's sake; for the imagination of man's heart is evil from his youth ; neither will I again smite any more every thing living, as I have done. Genesis 8:20-21
Abel was the first person in the Bible to kill and sacrifice an animal for God. His older brother, Cain, also sacrficed to God, but it was of vegetables, not meat. And the Lord preferred meat to veggies.
Cain brought of the fruit of the ground an offering unto the LORD. And Abel, he also brought of the firstlings of his flock and of the fat thereof. And the LORD had respect unto Abel and to his offering: But unto Cain and to his offering he had not respect. Genesis 4:2-5
Detailed instructions for animal sacrifice are provided in Leviticus. Here is just an example of the instructions that are given by God in the first nine chapters of Leviticus.
Kill the bullock before the LORD ... bring the blood, and sprinkle the blood round about upon the altar .. flay the burnt offering, and cut it into his pieces ... But his inwards and his legs shall he wash in water: and the priest shall burn all on the altar, to be a burnt sacrifice, an offering made by fire, of a sweet savour unto the LORD.Leviticus 1:5-9
The largest single animal sacrifice in the Bible (or probably anywhere) occurred when Solomon dedicated the temple, in which 142,000 animals were sacrificed to God.
King Solomon offered a sacrifice of twenty and two thousand oxen, and an hundred and twenty thousand sheep: so the king and all the people dedicated the house of God. 2 Chronicles 7:7 (See also 1 Kings 8:63)
For example, Mary and Joseph killed and sacrificed two turtledoves and two pigeons in the temple after Jesus's birth.
When the days of her purification according to the law of Moses were accomplished, they brought him to Jerusalem, to present him to the Lord ... to offer a sacrifice according to that which is said in the law of the Lord, A pair of turtledoves, or two young pigeons. Luke 2:21-24
Jesus told a man that he healed of leprosy to go to the temple and sacrifice some animals.
And it came to pass, when he was in a certain city, behold a man full of leprosy: who seeing Jesus fell on his face, and besought him, saying, Lord, if thou wilt, thou canst make me clean. And he put forth his hand, and touched him, saying, I will: be thou clean. And immediately the leprosy departed from him. And he charged him to tell no man: but go, and shew thyself to the priest, and offer for thy cleansing, according as Moses commanded, for a testimony unto them. Luke 5:12-14 (See also Matthew 8:1-4 and Mark 1:40-44)
According to the Synoptiic Gospels, Jesus and his disciples sacrificed a lamb for their Passober meal. (The Gospel of John disagrees, saying that Jesus died on the day the lambs were slaughtered in the temple -- the day before the Passover meal.)
Then came the day of unleavened bread, when the passover must be killed ... And they went, and found as he had said unto them: and they made ready the passover. Luke 22:7-13 (See also Matthew 26:17-30 and Mark 14:12-26)
Even Paul sacrificed some animals in the temple.
Then Paul took the men, and the next day purifying himself with them entered into the temple, to signify the accomplishment of the days of purification, until that an offering should be offered for every one of them. Acts 21:26
And Jesus, of course, was sacrificed to God at a human sacrifice. (And since humans are animals, this was also an animal sacrifice.)
Ye were not redeemed with corruptible things ... But with the precious blood of Christ, as of a lamb without blemish and without spot. 1 Peter 1:18