The General Instruction of the Roman Missal contains some introductory comments on the important role of Thanksgiving in the Mass:
#2 (Introduction): "...the Mass is at one and the same time a sacrifice of praise, thanksgiving, propitiation,
and satisfaction."
#72 (explaining the structure of the Ligurgy of the Eucharist):
"b) In the Eucharistic Prayer, thanks is given to God for the whole work of salvation, and the offerings become the Body and Blood of Christ."
#78 (introducing the Eucharistic Prayer): "Now the center and high point of the entire celebration begins, namely, the Eucharistic Prayer itself, that is, the prayer of thanksgiving and sanctification. The Priest calls upon the people to lift up
their hearts towards the Lord in prayer and thanksgiving..."
#79 (explaining the structure of the Eucharistic Prayer): "a) The thanksgiving (expressed especially in the Preface), in which the Priest, in the name of the
whole of the holy people, glorifies God the Father and gives thanks to him for the whole
work of salvation or for some particular aspect of it, according to the varying day, festivity,
or time of year.
#364 (on the choice of texts for Mass): "The numerous Prefaces with which the Roman Missal is endowed have as their purpose to bring
out more fully the motives for thanksgiving within the Eucharistic Prayer and to set out more clearly
the different facets of the mystery of salvation."
Not only is each Mass one great act of giving thanks to God, but we explicitly thank God at various times during the Mass.
Introductory Rites:
The "Gloria" (on Sundays outside of Advent and Lent): "...we give you thanks for your great glory..."
Liturgy of the Word:
After the First and Second Readings, the Lector proclaims, "The Word of the Lord"; and the assembly responds, "Thanks be to God."
Liturgy of the Eucharist:
In the "Preface," the priest says, "Let us give thanks to the Lord our God"; and the assembly responds, "It is right and just."
The priest then continues, "It is truly right and just, our duty and our salvation,
always and everywhere to give you thanks" (or similar words).
Each Eucharistic "Preface" then also explicitly mentions some thing(s) for which we are grateful to God.
Some Prefaces conclude with the words, "And so, Lord, with all the Angels and Saints, we, too, give you thanks, as in exultation we acclaim"
(other Prefaces similarly say that we "praise" or "acclaim" God).
In most of the Eucharistic Prayers, as the priest introduces the "Words of Institution" (spoken by Jesus over the bread and wine at the Last Supper) by explicitly recalling how Jesus "gave thanks" to God:
EP I: "giving you thanks, he said the blessing,
broke the bread
and gave it to his disciples..." / "once more giving you thanks, he said the blessing
and gave the chalice to his disciples..."
EP II: "he took bread and, giving thanks, broke it,
and gave it to his disciples..." / "he took the chalice
and, once more giving thanks,
he gave it to his disciples..."
EP III: "he himself took bread,
and, giving you thanks, he said the blessing,
broke the bread and gave it to his disciples..." / "he took the chalice,
and, giving you thanks, he said the blessing,
and gave the chalice to his disciples..."
EP IV: "while they were at supper,
he took bread, blessed and broke it,
and gave it to his disciples..." / "taking the chalice filled with the fruit of the vine,
he gave thanks,
and gave the chalice to his disciples..."
EP Reconciliation I: "he took bread
and, giving you thanks, he said the blessing,
broke the bread and gave it to them..." / "he took the chalice, filled with the fruit of the vine,
and once more giving you thanks,
handed the chalice to his disciples..."
EP Reconciliation II: "he himself took bread into his hands,
and, giving you thanks, he said the blessing,
broke the bread and gave it to his disciples" / "he took the chalice of blessing in his hands, confessing your mercy,
and gave the chalice to his disciples..."
EP Various Needs I-IV: "he took bread and said the blessing,
broke the bread and gave it to his disciples..." / "he took the chalice, gave you thanks
and gave the chalice to his disciples..."
Concluding Rites:
After the Final Blessing, the Deacon (or Priest) dismisses the Assembly, saying. "Go in peace, glorifying the Lord by your life" (or similar formulas); and the assembly responds, "Thanks be to God."
The Roman Missal also contains several prayers that a priest or any of the faithful could use for "Thanksgiving after Mass."
In addition to the above texts which are used at every Mass, in some Masses the Entrance Antiphon, the Collect, the Prayer over the Offerings, the Communion Antiphon, the Post-Communion Prayer, and a final Prayer over the People may also give thanks to God.
Moreover, at the Easter Vigil,
when the Deacon (or another minister) processes with the newly-blessed Easter Candle,
he three times proclaims "The Light of Christ" (Lumen Christi), and each time the assembly responds, "Thanks be to God" (Deo gratias).
Finally, two of the "Masses for Various Needs and Occasions" are focused on the theme of Thanksgiving (even more than every Mass does), in addition to the Mass for Thanksgiving Day (in the USA):
For Giving Thanks to
God for the Gift of Human Life (#48/1)
For Giving Thanks to God (#49)
Thanksgiving Day (4th Thursday of November)
Mercy & Forgiveness
(coming soon)
Participation:
(coming soon)
Silence:
The liturgical rubrics call for several periods of silent prayer and reflection during the Mass:
GIRM #45: "Sacred silence also, as part of the celebration, is to be observed at the designated times. Its nature, however, depends on the moment when it occurs in the different parts of the celebration. For in the Penitential Act and again after the invitation to pray, individuals recollect themselves; whereas after a reading or after the Homily, all meditate briefly on what they have heard; then after Communion, they praise God in their hearts and pray to him.
Even before the celebration itself, it is a praiseworthy practice for silence to be observed in the church, in the sacristy, in the vesting room, and in adjacent areas, so that all may dispose themselves to carry out the sacred celebration in a devout and fitting manner."
GIRM #56: "The Liturgy of the Word is to be celebrated in such a way as to favor meditation, and so any
kind of haste such as hinders recollection is clearly to be avoided. In the course of it, brief periods of
silence are also appropriate, accommodated to the assembled congregation; by means of these, under the action of the Holy Spirit, the Word of God may be grasped by the heart and a response through prayer may be prepared. It may be appropriate to observe such periods of silence, for example, before the Liturgy of the Word itself begins, after the First and Second Reading, and lastly at the conclusion of the Homily."
The following are the times that call for silence (at least optionally) in the Order of Mass:
Before Mass (GIRM #45, quoted above)
Beginning the Penitential Act (after the priest's introduction, "Let us acknowledge ous sins"): "A brief pause for silence follows." (RM #4, 5, 6; GIRM #51)
Before the Collect (after the priest says, "Let us pray"): "And all pray in silence with the Priest for a while." (RM #9; GIRM #54, 127)
Before the Liturgy of the Word begins (GIRM #56, quoted above)
After the First and Second Readings (GIRM #56, 128, 130)
After the Homily: "It is appropriate for a brief period of silence to be observed after the Homily." (GIRM #66, 136)
During the Universal Prayer (optional): "The people, for their part, stand and give expression to their prayer either by an invocation said
in common after each intention or by praying in silence."
During the Eucharistic Prayer: "The
Eucharistic Prayer requires that everybody listens to it with reverence and in silence." (GIRM #78, 147)
Before the priests receives Communion (GIRM #84)
At the end of the Communion Rite (RM #138; GIRM #43, 88, 164)
Before the Prayer after Communion (RM #139; GIRM #165, 271)
"Brief prayer in silence" is also recommended in the rubrics at various times during some special liturgies: Ash Wednesday, Palm Sunday, Holy Thursday, and especially on Good Friday and at the Easter Vigil.