The Introductory Rites of the Mass begin with the entrance song.  The clergy and other ministers process to and reverence the altar with a bow and/or kiss.  The altar is a symbol of Christ at the heart of the assembly. All make the Sign of the Cross. The celebrant greets the people with words from Scripture.

The Penitential Act at the beginning of Mass calls the faithful to recall their sins and to trust God's abiding mercy. The Penitential Act includes the Kyrie Eleison, a Greek phrase meaning, "Lord, have mercy."

On Sundays, solemnities, and feasts, the Gloria is next and is an ancient hymn that echoes the proclamation of the angels at the birth of Christ, "Glory to God in the highest!" and praises the Father, Son, and Holy Spirit.

The Introductory Rites conclude with an opening prayer, the Collect. The celebrant invites the assembly to pray and proclaims the prayer of the day.  The Collect gathers the prayers of all into one and disposes all to hear the Word of God.

The Liturgy of the Word is made up of readings from Scripture. The people are fed from the table of God's Word.  On Sundays and solemnities, there are three Scripture readings--the first is from the Old Testament, the second is from a New Testament letter, and the last is from one of the four Gospels.  The Scriptures are the word of God, inspired by the Holy Spirit, in which he speaks to the assembly of people and leads them to salvation.

The Responsorial Psalm is sung between the readings and helps the people to meditate on the word of God. 

The high point of the Liturgy of the Word is the reading of the Gospel. Because the Gospels tell of the life, ministry, and preaching of Christ, it receives special honor and reverence. The assembly stands and the Gospel is introduced by an acclamation of praise. Except during Lent, this praise is "Alleluia", derived from Hebrew that means "Praise the Lord!"  A deacon or priest reads the Gospel.

After the readings, the clergy preach the homily which focuses on the Scriptural texts and draws from them the lessons that may help the people to live more faithful, holy lives.

The Profession of Faith, either the Nicene Creed (dating from the 4th century) or the Apostles' Creed (an ancient baptismal creed of the Church of Rome) is recited by the assembly.

The Liturgy of the Word concludes with the Universal Prayer or the "Prayer of the Faithful" during which the assembly intercedes with God on behalf of the Church, the world, and themselves.

The Liturgy of the Eucharist begins with the preparation of the gifts and the altar. As the ministers prepare the altar, representatives of the people bring forward the bread and wine that will become the Body and Blood of Christ. The celebrant blesses and praises God for these gifts and places them on the altar.  Also, monetary gifts for the Church and the poor may be brought forward.

The Eucharistic Prayer is the heart of the Liturgy of the Eucharist. In this prayer, the celebrant acts in the person of Christ as head of his body, the Church.  He gathers the bread and the wine, and substance of our lives and joins them to Christ's perfect sacrifice, offering them to the Father. This prayer is offered in the presence of God and has thanksgiving as its central focus. The Eucharistic Prayers are offered to the Father by Christ as it was at the moment of his passion, death and resurrection, but now it is offered through the priest acting in the person of Christ, and it is offered by all of the baptized who are part of Christ's Body, the Church.  This is the action of Christ's Body, the Church, at Mass, and the "we" in the prayer signifies that all the baptized present make the sacrificial offering in union with Christ.  We do not offer Christ alone--we are called to offer ourselves, our lives, our efforts to grow in holiness, our efforts to spread God's Word, and our efforts to serve God's people. Our offering is imperfect, but when joined with the offering of Christ, it becomes perfect praise and thanksgiving to the Father.

The main elements of the Eucharistic Prayer are found in the General Instruction of the Roman Missal (no.79).  Summarized here, Thanksgiving, acclamation ("Holy, holy, holy , , ,") occur.  
Epiclesis involves the Church imploring the Holy Spirit to consecrate the gifts of bread and wine into Christ's Body and Blood and that this sacrificial offering to be consumed in Communion by the faithful will be for their salvation.
Institution narrative and Consecration of the bread and wine into the Body and Blood of Jesus Christ follow.
In Anamnesis that follows next, the Church fulfills Christ's command to celebrate the memorial of his Passion, Resurrection, and Ascension into heaven.
Oblation is the gathered Church's offering of the unblemished sacrifice to the Father though the Holy Spirit. The faithful offer this unblemished sacrificial Victim. They learn to offer themselves with the hope that, day by day, they will be brought into unity with God and with each other through the mediation of Christ and recognize that God is all in all.
Intercessions are the expression that the Eucharist is celebrated in communion with the whole Church in heaven and on earth, and that the oblation is made for her, the Church, and all her members, living and dead. All are called to participate in the redemption and salvation purchased by the Body and Blood of Christ.
The Concluding Doxology is the expression of the glory of God which is affirmed and concluded by the people's response, "Amen."

The Communion Rite follows the Eucharistic Prayer and leads the faithful to the Eucharistic table,  It begins with the Lord's Prayer as Jesus taught his disciples in Matt.6:9-13, Lk 11:2-4.

The Rite of Peace follows as the priest prays that the peace of Christ will fill the faithful. As a sign of hope, the people extend the sign of peace to others around them. This also calls to mind the greeting used by Christ Himself, "Peace be with you."

In the Fraction Rite, the priest breaks the consecrated bread, the Body of Christ, as the people sing the Agnus Dei or "Lamb of God", thus calling to mind Jn 1:29 in which John the Baptist proclaimed Jesus, "... the Lamb of God who takes away the sin of the world" as well as the actions of Jesus at the Last Supper when he broke the bread before giving it to his disciples in Lk 22:19. "Breaking of the bread" became synonymous with the early church's celebration in Lk 24:35, Acts 2:42,46.

Before receiving Holy Communion, the celebrant and assembly acknowledge their unworthiness to receive such a great gift in their posture and response, ". . . have mercy on me . . . "  The people approach the altar, bow with reverence, receive Holy Communion either on the tongue or in the hand as the priest, deacon or minister says, "The Body of Christ."  The communicant or the person receiving communion responds by affirming, "Amen" which is a Hebrew word meaning "So be it." 

The Communion Rite ends with the Prayer After Communion which asks for the benefits of the Eucharist to remain in the daily lives of the people.

During the Concluding Rites, announcements may be made after the Prayer After Communion. Then the celebrant prays for the blessing of the people, "May Almighty God bless you, the Father, and the Son, and the Holy Spirit."  The deacon dismisses the people.

"Mass" comes from the Latin word, "Missa."  Missa is related to the word 'missio" which is the root of the English "mission."  The Liturgy continues as those assembled are sent forth to bring the fruits of the Eucharist to the world.

Sources: USCCB, Sacrosanctum Concilium, no. 51; General Instruction of the Roman Missal no.79; Catechism of the Catholic Church, 2856; New American Bible.