Atonement can be described as the reconciliation of God with the Children of Israel through the Messiah Yahawashi. It is a day of fasting/afflicting your soul for a 24 hour period (from even to even) whereby nothing should enter into your mouth (no food, water or toothpaste, etc). This fast is mandatory for all Israelite born and is a day when The Most High will look upon us and give us a clean slate, once we have presented with a pure conscience and hear towards him. It is kept on the 10th day of the 7th month.
An excerpt from the Zondervan's Compact Bible Dictionary for atonement, Atonement day/Day of Atonement and Fasting.
Leviticus 16:29-34 And this shall be a statute for ever unto you: that in the seventh month, on the tenth day of the month, ye shall afflict your souls, and do no work at all, whether it be one of your own country, or a stranger that sojourneth among you:30 For on that day shall the priest make an atonement for you, to cleanse you, that ye may be clean from all your sins before the Lord.31 It shall be a sabbath of rest unto you, and ye shall afflict your souls, by a statute for ever.32 And the priest, whom he shall anoint, and whom he shall consecrate to minister in the priest's office in his father's stead, shall make the atonement, and shall put on the linen clothes, even the holy garments:33 And he shall make an atonement for the holy sanctuary, and he shall make an atonement for the tabernacle of the congregation, and for the altar, and he shall make an atonement for the priests, and for all the people of the congregation.34 And this shall be an everlasting statute unto you, to make an atonement for the children of Israel for all their sins once a year. And he did as the Lord commanded Moses.
Leviticus 23:26-32 And the Lord spake unto Moses, saying,27 Also on the tenth day of this seventh month there shall be a day of atonement: it shall be an holy convocation unto you; and ye shall afflict your souls, and offer an offering made by fire unto the Lord.28 And ye shall do no work in that same day: for it is a day of atonement, to make an atonement for you before the Lord your God.29 For whatsoever soul it be that shall not be afflicted in that same day, he shall be cut off from among his people.30 And whatsoever soul it be that doeth any work in that same day, the same soul will I destroy from among his people.31 Ye shall do no manner of work: it shall be a statute for ever throughout your generations in all your dwellings.32 It shall be unto you a sabbath of rest, and ye shall afflict your souls: in the ninth day of the month at even, from even unto even, shall ye celebrate your sabbath.
1Esdras 8:69-73 The nation of Israel, the princes, the priests and Levites, have not put away from them the strange people of the land, nor the pollutions of the Gentiles to wit, of the Canaanites, Hittites, Pheresites, Jebusites, and the Moabites, Egyptians, and Edomites. 70For both they and their sons have married with their daughters, and the holy seed is mixed with the strange people of the land; and from the beginning of this matter the rulers and the great men have been partakers of this iniquity. 71And as soon as I had heard these things, I rent my clothes, and the holy garment, and pulled off the hair from off my head and beard, and sat me down sad and very heavy. 72So all they that were then moved at the word of the Lord God of Israel assembled unto me, whilst I mourned for the iniquity: but I sat still full of heaviness until the evening sacrifice. 73Then rising up from the fast with my clothes and the holy garment rent, and bowing my knees, and stretching forth my hands unto the Lord,
Acts 27:9 Now when much time was spent, and when sailing was now dangerous, because the fast was now already past, Paul admonished them,
Exodus 30:10 And Aaron shall make an atonement upon the horns of it once in a year with the blood of the sin offering of atonements: once in the year shall he make atonement upon it throughout your generations: it is most holy unto the Lord.
Numbers 29:7 And ye shall have on the tenth day of this seventh month an holy convocation; and ye shall afflict your souls: ye shall not do any work therein:
Ezra 8:21 Then I proclaimed a fast there, at the river of Ahava, that we might afflict ourselves before our God, to seek of him a right way for us, and for our little ones, and for all our substance.
HOW TO OBSERVE
Psalm 81: 3 Blow up the trumpet in the new moon, in the time appointed, on our solemn feast day.
Judges 5:11 They that are delivered from the noise of archers in the places of drawing water, there shall they rehearse the righteous acts of the LORD, even the righteous acts toward the inhabitants of his villages in Israel: then shall the people of the LORD go down to the gates.
HOW TO FAST OR AFFLICT YOUR SOUL
BE HUMBLE AND SINCERE
Isaiah 66:2 For all those things hath mine hand made, and all those things have been, saith the Lord: but to this man will I look, even to him that is poor and of a contrite spirit, and trembleth at my word.
Psalm 51:17 The sacrifices of God are a broken spirit: a broken and a contrite heart, O God, thou wilt not despise.
Ecclesiasticus 35:16-17 He that serveth the Lord shall be accepted with favour, and his prayer shall reach unto the clouds.17The prayer of the humble pierceth the clouds: and till it come nigh, he will not be comforted; and will not depart, till the most High shall behold to judge righteously, and execute judgment.
EXAMINE YOURSELF AND CONFESS YOUR SINS
2Corinthians 13:5 Examine yourselves, whether ye be in the faith; prove your own selves. Know ye not your own selves, how that Jesus Christ is in you, except ye be reprobates?
Job 13:23 How many are mine iniquities and sins? make me to know my transgression and my sin.
Psalm 39:4-5 Lord, make me to know mine end, and the measure of my days, what it is: that I may know how frail I am.5 Behold, thou hast made my days as an handbreadth; and mine age is as nothing before thee: verily every man at his best state is altogether vanity. Selah.
1Kings 8:46-61 If they sin against thee, (for there is no man that sinneth not,) and thou be angry with them, and deliver them to the enemy, so that they carry them away captives unto the land of the enemy, far or near;47 Yet if they shall bethink themselves in the land whither they were carried captives, and repent, and make supplication unto thee in the land of them that carried them captives, saying, We have sinned, and have done perversely, we have committed wickedness;48 And so return unto thee with all their heart, and with all their soul, in the land of their enemies, which led them away captive, and pray unto thee toward their land, which thou gavest unto their fathers, the city which thou hast chosen, and the house which I have built for thy name:49 Then hear thou their prayer and their supplication in heaven thy dwelling place, and maintain their cause,50 And forgive thy people that have sinned against thee, and all their transgressions wherein they have transgressed against thee, and give them compassion before them who carried them captive, that they may have compassion on them:51 For they be thy people, and thine inheritance, which thou broughtest forth out of Egypt, from the midst of the furnace of iron:52 That thine eyes may be open unto the supplication of thy servant, and unto the supplication of thy people Israel, to hearken unto them in all that they call for unto thee.53 For thou didst separate them from among all the people of the earth, to be thine inheritance, as thou spakest by the hand of Moses thy servant, when thou broughtest our fathers out of Egypt, O Lord God.54 And it was so, that when Solomon had made an end of praying all this prayer and supplication unto the Lord, he arose from before the altar of the Lord, from kneeling on his knees with his hands spread up to heaven.55 And he stood, and blessed all the congregation of Israel with a loud voice, saying,56 Blessed be the Lord, that hath given rest unto his people Israel, according to all that he promised: there hath not failed one word of all his good promise, which he promised by the hand of Moses his servant.57 The Lord our God be with us, as he was with our fathers: let him not leave us, nor forsake us:58 That he may incline our hearts unto him, to walk in all his ways, and to keep his commandments, and his statutes, and his judgments, which he commanded our fathers.59 And let these my words, wherewith I have made supplication before the Lord, be nigh unto the Lord our God day and night, that he maintain the cause of his servant, and the cause of his people Israel at all times, as the matter shall require:60 That all the people of the earth may know that the Lord is God, and that there is none else.61 Let your heart therefore be perfect with the Lord our God, to walk in his statutes, and to keep his commandments, as at this day.
TASTE NOTHING
Jonah 3:4-6 And Jonah began to enter into the city a day's journey, and he cried, and said, Yet forty days, and Nineveh shall be overthrown.5 So the people of Nineveh believed God, and proclaimed a fast, and put on sackcloth, from the greatest of them even to the least of them.6 For word came unto the king of Nineveh, and he arose from his throne, and he laid his robe from him, and covered him with sackcloth, and sat in ashes.
EVEN TO EVEN
Leviticus 23:32 It shall be unto you a sabbath of rest, and ye shall afflict your souls: in the ninth day of the month at even, from even unto even, shall ye celebrate your sabbath.
NO DOING YOUR OWN PLEASURE/NO SEX DURING THE FAST/NO PLAYING GAME ETC
Isaiah 58:2-8 Yet they seek me daily, and delight to know my ways, as a nation that did righteousness, and forsook not the ordinance of their God: they ask of me the ordinances of justice; they take delight in approaching to God.3 Wherefore have we fasted, say they, and thou seest not? wherefore have we afflicted our soul, and thou takest no knowledge? Behold, in the day of your fast ye find pleasure, and exact all your labours.4 Behold, ye fast for strife and debate, and to smite with the fist of wickedness: ye shall not fast as ye do this day, to make your voice to be heard on high.5 Is it such a fast that I have chosen? a day for a man to afflict his soul? is it to bow down his head as a bulrush, and to spread sackcloth and ashes under him? wilt thou call this a fast, and an acceptable day to the LORD?6 Is not this the fast that I have chosen? to loose the bands of wickedness, to undo the heavy burdens, and to let the oppressed go free, and that ye break every yoke?7 Is it not to deal thy bread to the hungry, and that thou bring the poor that are cast out to thy house? when thou seest the naked, that thou cover him; and that thou hide not thyself from thine own flesh?8 Then shall thy light break forth as the morning, and thine health shall spring forth speedily: and thy righteousness shall go before thee; the glory of the LORD shall be thy reward.
1Corinthians 7:5 Defraud ye not one the other, except it be with consent for a time, that ye may give yourselves to fasting and prayer; and come together again, that Satan tempt you not for your incontinency.
NO KINDLING FIRE
Exodus 35:3 Ye shall kindle no fire throughout your habitations upon the sabbath day.
NO BUYING OR SELLING
Nehemiah 10:31 And if the people of the land bring ware or any victuals on the sabbath day to sell, that we would not buy it of them on the sabbath, or on the holy day: and that we would leave the seventh year, and the exaction of every debt.
BEAR NO BURDEN
Jeremiah 17:21-24 Thus saith the Lord; Take heed to yourselves, and bear no burden on the sabbath day, nor bring it in by the gates of Jerusalem;22 Neither carry forth a burden out of your houses on the sabbath day, neither do ye any work, but hallow ye the sabbath day, as I commanded your fathers.23 But they obeyed not, neither inclined their ear, but made their neck stiff, that they might not hear, nor receive instruction.24 And it shall come to pass, if ye diligently hearken unto me, saith the Lord, to bring in no burden through the gates of this city on the sabbath day, but hallow the sabbath day, to do no work therein;
NO WORK
Leviticus 23:2-3 Speak unto the children of Israel, and say unto them, Concerning the feasts of the LORD, which ye shall proclaim to be holy convocations, even these are my feasts.3 Six days shall work be done: but the seventh day is the sabbath of rest, an holy convocation; ye shall do no work therein: it is the sabbath of the LORD in all your dwellings.
BE OCCUPIED IN THE SCRIPTURES
Joshua 1:8 This book of the law shall not depart out of thy mouth; but thou shalt meditate therein day and night, that thou mayest observe to do according to all that is written therein: for then thou shalt make thy way prosperous, and then thou shalt have good success.
WASH UP AND NOT APPEAR TO FAST
Matthew 6:16-18 Moreover when ye fast, be not, as the hypocrites, of a sad countenance: for they disfigure their faces, that they may appear unto men to fast. Verily I say unto you, They have their reward.17 But thou, when thou fastest, anoint thine head, and wash thy face;18 That thou appear not unto men to fast, but unto thy Father which is in secret: and thy Father, which seeth in secret, shall reward thee openly.
PRAYER IS GOOD WITH FASTING
Tobit 12:8 Prayer is good with fasting and alms and righteousness. A little with righteousness is better than much with unrighteousness. It is better to give alms than to lay up gold:
PREPARE WHAT TO SAY
Ecclesiasticus 33:4 Prepare what to say, and so thou shalt be heard: and bind up instruction, and then make answer.
Ecclesiasticus 7:14 Use not many words in a multitude of elders, and make not much babbling when thou prayest.
FORGIVE AND LET GO OF ANY GRUDGE YOU MAY HAVE WITH ANY
Matthew 6:14-15 For if ye forgive men their trespasses, your heavenly Father will also forgive you:15 But if ye forgive not men their trespasses, neither will your Father forgive your trespasses.