Please note: the first video contains only the Offertory.
The second video contains both Offertory and Eucharistic Prayer.

What is the Offertory Chant and when does it begin? (GIRM 139) When the Universal Prayer is over, all sit, and the Offertory Chant begins (cf. no. 74).

How long should the Offertory Chant last? (GIRM 74) The procession bringing the gifts is accompanied by the Offertory Chant (cf. no. 37 b), which continues at least until the gifts have been placed on the altar. The norms on the manner of singing are the same as for the Entrance Chant (cf. no. 48). Singing may always accompany the rite at the Offertory, even when there is no procession with the gifts.

How is the Offertory Chant chosen? The same critera as the Entrance Chant. (GRIM 48) This chant is sung alternately by the choir and the people or similarly by a cantor and the people, or entirely by the people, or by the choir alone.

In the Dioceses of the United States of America there are four options for the Entrance Chant:

(1) the antiphon from the Missal or the antiphon with its Psalm from the Graduale Romanum as set to music there or in another setting;
(2) the antiphon and Psalm of the Graduale Simplex for the liturgical time;
(3) a chant from another collection of Psalms and antiphons, approved by the Conference of Bishops or the Diocesan Bishop, including Psalms arranged in responsorial or metrical forms;
(4) another liturgical chant that is suited to the sacred action, the day, or the time of year, similarly approved by the Conference of Bishops or the Diocesan Bishop.

What do the servers do during the Offertory Chant? An acolyte or other lay minister places the corporal, the purificator, the chalice, the pall, and the Missal on the altar.

What do the faithful do during the Offertory Chant? (GIRM 140) It is desirable that the participation of the faithful be expressed by an offering, whether of bread and wine for the celebration of the Eucharist or of other gifts to relieve the needs of the Church and of the poor. The offerings of the faithful are received by the Priest, assisted by the acolyte or other minister. The bread and wine for the Eucharist are carried to the Celebrant, who places them on the altar, while other gifts are put in another suitable place (cf. no. 73).

What is a suitable place? (GIRM 73) At the beginning of the Liturgy of the Eucharist the gifts which will become Christ’s Body and Blood are brought to the altar. First of all, the altar or Lord’s table, which is the center of the whole Liturgy of the Eucharist, is made ready when on it are placed the corporal, purificator, Missal, and chalice (unless this last is prepared at the credence table). The offerings are then brought forward. It is a praiseworthy practice for the bread and wine to be presented by the faithful. They are then accepted at an appropriate place by the Priest or the Deacon to be carried to the altar. Even though the faithful no longer bring from their own possessions the bread and wine intended for the liturgy as was once the case, nevertheless the rite of carrying up the offerings still keeps its spiritual efficacy and significance. Even money or other gifts for the poor or for the Church, brought by the faithful or collected in the church, are acceptable; given their purpose, they are to be put in a suitable place away from the Eucharistic table.

Why is the suitable place away from the Eucharistic table?

If the Offertory Chant continues, what is the priest doing and praying at this time? What are the servers doing? (GIRM 141 & 142) The Priest accepts the paten with the bread at the altar, holds it slightly raised above the altar with both hands and says quietly, Benedictus es, Domine (Blessed are you, Lord God). Then he places the paten with the bread on the corporal. After this, as the minister presents the cruets, the Priest stands at the side of the altar and pours wine and a little water into the chalice, saying quietly, Per huius aquae (By the mystery of this water). He returns to the middle of the altar and with both hands raises the chalice a little, and says quietly, Benedictus es, Domine (Blessed are you, Lord God). Then he places the chalice on the corporal and, if appropriate, covers it with a pall.

What are the servers doing at this time? What is incensed and why? Does incense have to be used? (GIRM 75) The bread and wine are placed on the altar by the Priest to the accompaniment of the prescribed formulas; the Priest may incense the gifts placed on the altar and then incense the cross andthe altar itself, so as to signify the Church’s offering and prayer rising like incense in the sight of God. Next, the Priest, because of his sacred ministry, and the people, by reason of their baptismal dignity, may be incensed by the Deacon or by another minister.

Why do the people sometime say prayers at this point of the Mass? (GIRM 143-145) If, however, there is no Offertory Chant and the organ is not played, in the presentation of the bread and wine the Priest may say the formulas of blessing aloud and the people acclaim, Blessed be God for ever. After placing the chalice on the altar, the Priest bows profoundly and says quietly, In spiritu humilitatis (With humble spirit). If incense is being used, the Priest then puts some in the thurible, blesses it without saying anything, and incenses the offerings, the cross, and the altar. While standing at the side of the altar, a minister incenses the Priest and then the people. After the prayer In spiritu humilitatis (With humble spirit) or after the incensation, the Priest washes his hands standing at the side of the altar and, as the minister pours the water, says quietly, Lava me, Domine (Wash me, O Lord).