In the New Covenant, prayer is the living relationship of the children of God with their Father who is good beyond measure, with his Son Jesus Christ and with the Holy Spirit. The grace of the Kingdom is "the union of the entire holy and royal Trinity . . . with the whole human spirit." Thus, the life of prayer is the habit of being in the presence of the thrice-holy God and in communion with him. This communion of life is always possible because, through Baptism, we have already been united with Christ. Prayer is Christian insofar as it is communion with Christ and extends throughout the Church, which is his Body. Its dimensions are those of Christ's love. (Catechism of the Catholic Church, n.2565)
The fundamental Christian prayer is The Lord's Prayer, the "Our Father"
Our Father who art in heaven,
hallowed be thy name.
Thy kingdom come.
Thy will be done on earth, as it is in heaven.
Give us this day our daily bread,
and forgive us our trespasses,
as we forgive those who trespass against us,
and lead us not into temptation,
but deliver us from evil.
The teaching on prayer in the Catechism of the Catholic Church is built upon the petitions of The Lord's Prayer.
The Prayer of the Church
“From ancient times the Church has had the custom of celebrating each day the liturgy of the hours. In this way the Church fulfills the Lord’s precept to pray without ceasing, at once offering its praise to God the Father and interceding for the salvation of the world.” – Office of the Sacred Congregation for Divine Worship.
Other Catholic Prayers
Traditional Catholic Prayers and Devotions- from the US Conference of Catholic Bishops
Catholic Prayers - from St. Charles Borromeo Church, Picayune, Mississippi
Catholic Prayers - from EWTN
Catholic Prayers - from CatholiCity
We highly recommend this prayer book: Catholic Household Blessings and Prayers from the USCCB
Resources on Prayer and Liturgy