During Old Testament times, God instructed the Israelites to make sacrifices and offerings for the purpose of teaching people about sin and the need for atonement of sins.
The Israelites would bring their offerings to Levitical priests, who would slaughter the animals and offer them to God for atonement.
The burnt offering was an overall offering used to sacrifice to God. The concept was that when a person approached the perfect and holy God, he needed to bring a sacrificial animal to make general atonement for his sins. This bridged the gap between God and man temporarily in ancient times.
The whole burnt offering was a complete destruction of an animal (except for the hide which was given to the priest as part of his wages).
The grain offering was made as an offering to God to thank Him for His provisions. The Israelites made a grain offering of early ripened things to thank God for their harvest (Leviticus 2:14). It was similar to a free-will offering. Also, if a person was poor, he could offer a grain offering instead of a bull or doves (Leviticus 5:13).
As for the sin offering and guilt offering, these were somewhat similar. When a person realized he had sinned against God, he was instructed to make a sacrifice to God. A sin offering was mostly made for unintentional sins (Leviticus 4:27).
A guilt offering was made for sins committed against God or man that needed not only to make atonement for, but also to make reparations for. Examples of this included robbery and lying under oath, which were more serious sins. The sinner was instructed to make restitution in full plus one-fifth more (Leviticus 6:5). Other sins that required a guilt offering included accidentally violating God's holy things (Leviticus 5:14-15).
You can read more about these offerings and their appointed times below. The grain offering could be offered whenever a person wanted. The sin and guilt offerings were offered after a person realized he sinned.
https://www.gotquestions.org/burnt-offering.html
https://www.gotquestions.org/grain-offering.html
https://www.gotquestions.org/sin-offering.html
https://www.gotquestions.org/trespass-offering.html
You may wonder: What about intentional sins that were very serious, such as murder or idolatry? Were there offerings for those?
Such sins had no sacrifice to atone for in Old Testament times. People were put to death for these intentional serious sins.
"If anyone kills a person, the murderer shall be put to death at the evidence of witnesses, but no person shall be put to death on the testimony of one witness." (Numbers 35:30)
"If there is found in your midst, in any of your towns, which the Lord your God is giving you, a man or a woman who does what is evil in the sight of the Lord your God, by transgressing His covenant, and has gone and served other gods and worshiped them, or the sun or the moon or any of the heavenly host, which I have not commanded, and if it is told you and you have heard of it, then you shall inquire thoroughly. Behold, if it is true and the thing certain that this detestable thing has been done in Israel, then you shall bring out that man or that woman who has done this evil deed to your gates, that is, the man or the woman, and you shall stone them to death." (Deuteronomy 17:2-5)
"If there is anyone who curses his father or his mother, he shall surely be put to death; he has cursed his father or his mother, his bloodguiltiness is upon him." (Leviticus 20:9)
The Old Testament sacrificial system was limited in that some sins were atoned for temporarily through animal sacrifices, while other sins could not be atoned for. For those sins that had no atonement, the guilty person got punished for what he did.
"The judges shall investigate thoroughly, and if the witness is a false witness and he has accused his brother falsely, then you shall do to him just as he had intended to do to his brother. Thus you shall purge the evil from among you. The rest will hear and be afraid, and will never again do such an evil thing among you. Thus you shall not show pity: life for life, eye for eye, tooth for tooth, hand for hand, foot for foot." (Deuteronomy 19:18-21)
So each sin was punished, either in a substitutionary way through an animal or directly on the sinner.
And God has not changed or lowered His justice. The instructions for animal sacrifices were given to teach people the need for atonement of sins and the need for a Savior, because animals could not truly atone for sins.
That is why Jesus, the perfect Son of God, came and made atonement for our sins on our behalf. All the sins we have committed (no matter how serious) were nailed to the cross.
Jesus suffered so much for us beyond what we can understand. He suffered in His spirit and physically (Isaiah 53:11), and He was disfigured beyond recognition (Isaiah 52:14).
Through His sacrifice, He justified all who believe in Him.
"For it is impossible for the blood of bulls and goats to take away sins." (Hebrews 10:4)
The use of animal sacrifices was to point people to the need for a Savior. When the Savior came, He took away the sins of all who were looking for Him and believed in Him.
"Every priest stands daily ministering and offering time after time the same sacrifices, which can never take away sins; but He, having offered one sacrifice for sins for all time, sat down at the right hand of God, waiting from that time onward until His enemies be made a footstool for His feet. For by one offering He has perfected for all time those who are sanctified." (Hebrews 10:11-14)
So if we believe in Jesus, we do not need to offer burnt, sin, or guilt offerings to God. Jesus became the sacrificial "Lamb of God who takes away the sin of the world!" (John 1:29).
All we need to do is trust Jesus for salvation, repent (turn away) from our sins, and follow Him!