Sancta Missa has some excellent articles available on their site.
Take for example this brief explanation of the Prayers at the Foot of the Altar, which was part of the Mass from about the third centuries until 1970, from Explanation of the Prayers and Ceremonies of Holy Mass.
Prayers at the foot of the Altar
Holy Church here makes use of the formula of confession, which she has drawn up; it probably dates from the 8th century. We are not allowed to make the slightest change in the words. It has this prerogative, in common with all the other Sacramentals, – that its recitation produces the forgiveness of venial sins, provided we be contrite for them. Thus it is, that God, in His Infinite Goodness, has provided us with other means, over and above the Sacrament of Penance, whereby we may be cleansed from our venial sins: He, for this end, inspired His Church to give us her Sacramentals.
The Priest, as we were saying, begins the confession; and, first of all, he accuses himself to God. But, he is not satisfied with that; – he as good as says: “I not only desire to confess my sins to God, but to all the Saints; in order that they may join their prayers with mine, and obtain pardon for me.” Therefore, he immediately adds: “I confess to the Blessed Mary ever Virgin.” Not that he has ever committed any offence against this holy Mother; but he has sinned in her sight; and the very thought of it urges him to make his sins known to Her also.
He does the same to the glorious St. Michael, the great Archangel, who is appointed to watch over our souls, especially at the hour of death. In like manner, he confesses to St. John the Baptist, who was so dear to our Lord, and was His precursor. Lastly, he desires to own his sins to Saints Peter and Paul, the two Princes of the Apostles. Certain Religious Orders have permission to add the name of their Patriarch or Founder. Thus, the Benedictines insert the name of St. Benedict; the Dominicans, St. Dominic; the Franciscans, St. Francis. After mentioning these and all the Saints, he would have even the Faithful, who are present, know that he is a sinner; and he therefore says to them: And to you, Brethren! because, as he is now humbling himself on account of his sins, he not only accuses himself before those who are glorified in God, but moreover, before those his fellow-mortals who are there visibly present, near the sanctuary.
And not satisfied with declaring himself to be a sinner, he adds in what way he has sinned; and confesses, that it is by all the three ways, wherein men commit sin, namely, by thought, word, and deed: cogitatione, verbo, et opere. Then wishing to express, that he has thus sinned and through his own freewill, be utters these words: Mea culpa, mea culpa, mea maxima culpa: through my fault, through my fault, through my most grievous fault.
And, that he may, like the publican of the Gospel, outwardly testify his inward repentance, he thrice strikes his breast, whilst saying those words. Conscious of the need he has of pardon, he once more turns towards Mary and all the Saints, as likewise to the Faithful who are present, begging that they will all pray for him. In reference to this formula of Confession, which has been established by our holy Mother the Church, it may be well to remind our readers, that it would, of itself, suffice for one who was in danger of death, and unable to make a more explicit Confession.
The Ministers answer the Priest by wishing him the grace of God’s mercy; they express their wish under the form of prayer, during which he, the Priest, remains bowed down, and answers: Amen.
But, the Ministers themselves stand in need of God’s pardon; and, therefore, they repeat the same formula as the Priest, for the confession of their sins; only, instead of saying: Et vobis, fratres, and to you, Brethren, they address the Priest, and call him Father: Et tibi, Pater.
It is never allowable to change anything which holy Church has prescribed for the celebration of the Mass. Hence, in the Confiteor, the Ministers must always use the simple words: Et tibi, Pater; Et te, Pater; they must add no further title, not even were they serving the Pope’s Mass.
As soon as the Ministers have finished the Confession formula, the Priest says the same prayer for them, as they had previously made for him; and they, also, respond to it by an Amen. A sort of blessing then follows: Indulgentiam, &c., whereby the Priest asks, both for himself and his brethren, pardon and forgiveness of their sins; he makes the sign of the Cross, and uses the word nobis and not vobis, for he puts himself on an equality with his Ministers, and takes his share in the prayer that is said for all.
The Confession having been made, the Priest again bows down, but not so profoundly as he did during the Confiteor. He says: Deus, tu conversus vivificabis nos: Thou, O God, with one look, wilt give us life; to which the Ministers answer: Et plebs tua laetabitur in te: And thy people will rejoice in thee. Then, – Ostende nobis, Domine, misericordiam tuam: Show unto us thy mercy, O Lord; Et salutare tuum da nobis: And grant us the Saviour whom thou hast prepared for us.
The practice of reciting these Versicles is very ancient. The last gives us the words of David, who, in his 84th Psalm, is praying for the coming of the Messias. In the Mass, before the Consecration, we await the coming of our Lord, as they, who lived before the Incarnation, awaited the promised Messias. By that word Mercy, which is here used by the Prophet, we are not to understand the Goodness of God; but, we ask of God, that He will vouchsafe to send us Him, who in His Mercy and His Salvation, that is to say, the Saviour, by whom Salvation is to come upon us. These few words of the Psalm take us back in spirit, to the Season of Advent, when we are unceasingly asking for him who is to come.
After this, the Priest asks of God, that He would vouchsafe to grant his prayer: Domine, exaudi orationem meam: Lord, hear my prayer. The Ministers continue, as though in his name: Et clamor meus ad te veniat: And let my cry come unto thee. The Priest salutes the people, saying: Dominus vobiscum: The Lord be with you. It is as though he were taking leave of them, now that the solemn moment is come for him to ascend the Altar, and, like Moses, enter into the cloud. The Ministers answer him in the name of the people: Et cum spiritu tuo: And with thy spirit.
Whilst going up to the Altar, the Priest says Oremus: he stretches out his hands, and joins them again. As often as he uses this word, he observes the same ceremony. The reason is, that it immediately precedes some prayer which he is going to make; and, when we pray, we raise our hands up to God, who is in heaven, and to whom we are about to speak.
It was thus that our Blessed Lord prayed on the Cross. In the prayer, which the Priest says, whilst ascending the Altar- steps, he uses the plural, because he is not alone; for the Deacon and Subdeacon go up together with him, and minister to him. The thought which is uppermost in the Priest’s mind, at this solemn moment is, to be all pure; for, as he says, he is entering into the Holy of Holies: Ad Sancta Sanctorum, meaning to express, by this Hebrew superlative, the importance of the act which he is going to fulfil. He prays, therefore, that his sins, as well as those of his Ministers, may be taken away. T
he nearer we approach to God, the more we feel the slightest sin to be an intolerable blot upon our soul; so that the Priest redoubles his prayer, that God would cleanse him from his sins. He has already prayed this merciful Lord to turn and give him life; Deus tu conversus vivificabis nos. – Ostende nobis Domine misericordiam tuam. But, having drawn nearer to that God, his fear increases, and his desire of pardon is more ardent; he repeats this same prayer again now whilst going up the Altar-steps. Having reached the Altar, he puts his hands upon it, first joined, and then separated, so that he may kiss it.
This kissing the Altar is prompted by a sentiment of respect for the Saints’ Relics, which are there. Again, another prayer for pardon of his sins: in it, he says: peccata mea: my sins; although he began it by: Oramus Te, Domine: We beseech thee, O Lord; nor is there any inadvertency in this; for, all those who assist at the holy Sacrifice should entertain, for the Priest, a sentiment of filial respect, and pray with and for him.