“Then Jesus was led by the spirit into the desert, to be tempted by the devil. And when he had fasted forty days and forty nights, afterwards he was hungry.”
St. Matthew

1. Tradition and Canon Law

Christians have always set aside Wednesdays and Fridays as penitential days. Wednesday was the day Our Lord was betrayed and Friday was the day Our Lord was crucified. In most Eastern Catholic churches and Orthodox churches Wednesdays and Fridays are still days of penance. In the Latin Church, only Fridays remain as weekly penitential days on which abstinence from meat and other forms of penance are performed.
1983 Code of Canon Law:
Can. 1250 The days and times of penance for the universal Church are each Friday of the whole year and the season of Lent.
Can. 1251 Abstinence from meat, or from some other food as determined by the Episcopal Conference, is to be observed on all Fridays, unless a solemnity should fall on a Friday. Abstinence and fasting are to be observed on Ash Wednesday and Good Friday.

2. Abstinence

In the Latin Church, abstinence means refraining from eating the meat from mammals or fowl, and soup or gravy made with them. Fish is allowed; traditionally, the laws of abstinence apply to all aged seven and over, but the new Code of Canon Law applies it to all who are fourteen and over. Partial abstinence consists of meat and soup or gravy made from meat may be eaten, but only once a day and at the principle meal.

3. Fasting

Fasting is the taking of only one full meal (may include meat) and two smaller meals (meatless) that must be smaller to the lager meal. No snacking between meals is allowed, but water, milk, tea, coffee, and juices are fine. Meat is allowed at one meal, only.
We are to abstain and fast on Ash Wednesday. During the Lenten embertide traditional Catholics abstain and fast- the Lenten Embertide is nonexistent in the Mass of Paul VI. All days of Lent but Fridays, Saturdays, Sundays and First Class feast; traditional Catholic partially abstain and fast, Catholic who attend the Mass of Paul VI need not do anything for it is not required anymore. Fridays and Saturdays of Lent traditional Catholics abstain and fast; 1983 Code requires those who attend the Mass of Paul VI to abstain on Fridays (not Saturdays). On Good Friday, both traditionalists and other Roman Rite Catholic abstain and fast. On Holy Saturday, traditionalists abstain and fast until after the Vigil Mass; again, for those who attend the Mass of Paul VI, this is not required.

4. The Holy Law of Fasting

Pope Clement XIII, Appetente Sacro, 1759 decribes the reason for fasting:

Pope Clement XIII

“You will begin most appropriately, and with hope of the greatest profit, to recall men to the observance of the holy law of fasting, if you teach the people this: penance for the Christian man is not satisfied by withdrawing from sin, by detesting a past life badly lived, or by the sacramental confession of these same sins. Rather, penance also demands that we satisfy divine justice with fasting, almsgiving, prayer, and other works of the spiritual life. Every wrongdoing — be it large or small — is fittingly punished, either by the penitent or by a vengeful God. Therefore we cannot avoid God’s punishment in any other way than by punishing ourselves.”
“If this teaching is constantly implanted in the minds of the faithful, and if they drink deeply of it, there will be very little cause to fear that those who have discarded their degraded habits and washed their sins clean through sacramental confession would not want to expiate the same sins through fasting, to eliminate the concupiscence of the flesh. Besides, consider the man who is convinced that he repents of his sins more firmly when he does not allow himself to go unpunished. That man, already consumed with the love of penance, will rejoice during the season of Lent and on certain other days, when the Church declares that the faithful should fast and gives them the opportunity to bring forth worthy fruits of penance.”

5. The “Golden Mouth” on Fasting

St. John Chrysostom sums up the attitude we should have when fasting:
7. …We have this fast too as an ally, and as an assistant in this good intercession. Therefore, as when the winter is over and the summer is appearing, the sailor draws his vessel to the deep; and the soldier burnishes his arms, and makes ready his steed for the battle; and the husbandman sharpens his sickle; and the traveller boldly undertakes a long journey, and the wrestler strips and bares himself for the contest. So too, when the fast makes its appearance, like a kind of spiritual summer, let us as soldiers burnish our weapons; and as husbandmen let us sharpen our sickle; and as sailors let us order our thoughts against the waves of extravagant desires; and as travellers let us set out on the journey towards heaven; and as wrestlers let us strip for the contest. For the believer is at once a husbandman, and a sailor, and a soldier, a wrestler, and a traveller. Hence St. Paul saith, “We wrestle not against flesh and blood, but against principalities, against powers. Put on therefore the whole armour of God.” Hast thou observed the wrestler? Hast thou observed the soldier? If thou art a wrestler, it is necessary for thee to engage in the conflict naked. If a soldier, it behoves thee to stand in the battle line armed at all points. How then are both these things possible, to be naked, and yet not naked; to be clothed, and yet not clothed! How? I will tell thee. Divest thyself of worldly business, and thou hast become a wrestler.
Put on the spiritual armour, and thou hast become a soldier. Strip thyself of worldly cares, for the season is one of wrestling. Clothe thyself with the spiritual armour, for we have a heavy warfare to wage with demons. Therefore also it is needful we should be naked, so as to offer nothing that the devil may take hold of, while he is wrestling with us; and to be fully armed at all points, so as on no side to receive a deadly blow. Cultivate thy soul. Cut away the thorns. Sow the word of godliness. Propagate and nurse with much care the fair plants of divine wisdom, and thou hast become a husbandman. And Paul will say to thee, “The husbandman that laboureth must be first partaker of the fruits. He too himself practised this art. Therefore writing to the Corinthians, he said, “I have planted, Apollos watered, but God gave the increase.” Sharpen thy sickle, which thou hast blunted through gluttony–sharpen it by fasting. Lay hold of the pathway which leads towards heaven; rugged and narrow as it is, lay hold of it, and journey on. And how mayest thou be able to do these things? By subduing thy body, and bringing it into subjection. For when the way grows narrow, the corpulence that comes of gluttony is a great hindrance. Keep down the waves of inordinate desires. Repel the tempest of evil thoughts. Preserve the bark; display much skill, and thou hast become a pilot. But we shall have the fast for a groundwork and instructor in all these things.

Portrait of Saint John Chrysostom of Antioch (Hagios Ioannis Chrysostomos). An early Byzantine mosaic from the Cathedral of Hagia Sophia in Constantinople (modern Istanbul).

8. I speak not, indeed, of such a fast as most persons keep, but of real fasting; not merely an abstinence from meats; but from sins too. For the nature of a fast is such, that it does not suffice to deliver those who practice it, unless it be done according to a suitable law. “For the wrestler,” it is said, “is not crowned unless he strive lawfully.” To the end then, that when we have gone through the labour of fasting, we forfeit not the crown of fasting, we should understand how, and after what manner, it is necessary to conduct this business; since that Pharisee also fasted, but afterwards when down empty, and destitute of the fruit of fasting. The Publican fasted not; and yet he was accepted in preference to him who had fasted; in order that thou mayest learn that fasting is unprofitable, except all other duties follow with it. The Ninevites fasted, and won the favour of God. The Jews fasted too, and profited nothing, nay they departed with blame. Since then the danger in fasting is so great to those who do not know how they ought to fast, we should learn the laws of this exercise, in order that we may not “run uncertainly,” nor “beat the air,” nor while we are fighting contend with a shadow. Fasting is a medicine; but a medicine, though it be never so profitable, becomes frequently useless owing to the unskillfulness of him who employs it. For it is necessary to know, moreover, the time when it should be applied, and the requisite quantity of it; and the temperament of body that admits it; and the nature of the country, and the season of the year; and the corresponding diet; as well as various other particulars; any of which, if one overlooks, he will mar all the rest that have been named. Now if, when the body needs healing, such exactness is required on our part, much more ought we, when our care is about the soul, and we seek to heal the distempers of the mind, to look, and to search into every particular with the utmost accuracy.
11. I have said these things, not that we may disparage fasting, but that we may honour fasting; for the honour of fasting consists not in abstinence from food, but in withdrawing from sinful practices; since he who limits his fasting only to an abstinence from meats, is one who especially disparages it. Dost thou fast? Give me proof of it by thy works! Is it said by what kind of works? If thou seest a poor man, take pity on him! If thou seest an enemy, be reconciled to him! If thou seest a friend gaining honour, envy him not! If thou seest a handsome woman, pass her by! For let not the mouth only fast, but also the eye, and ear, and the feet, and the hands, and all the members of our bodies. Let the hands fast, by being pure from rapine and avarice. Let the feet fast, but ceasing from running to the unlawful spectacles. Let the eyes fast, being taught never to fix themselves rudely upon handsome countenances, or to busy themselves with strange beauties. For looking is the food of the eyes, but if this be such as is unlawful or forbidden, it mars the fast; and upsets the whole safety of the soul; but if it be lawful and safe, it adorns fasting. For it would be among things the most absurd to abstain from lawful food because of the fast, but with the eyes to touch even what is forbidden. Dost thou not eat flesh? Feed not upon lasciviousness by means of the eyes. Let the ear fast also. The fasting of the ear consists in refusing to receive evil speakings and calumnies. “Thou shalt not receive a false report,” it says.