First stop IMO is the CCC. It speaks a great deal on contemplative prayer, more than vocal and meditative combined, in
“Expressions of Prayer” CCC 2700-2724. Note in 2708 it points out Christian prayer “should” include this form of prayer.
Sample paragraphs:
2709 What is contemplative prayer? St. Teresa answers: "Contemplative prayer [oracion mental] in my opinion is nothing else than a close sharing between friends; it means taking time frequently to be alone with him who we know loves us."6 Contemplative prayer seeks him "whom my soul loves."7 It is Jesus, and in him, the Father. We seek him, because to desire him is always the beginning of love, and we seek him in that pure faith which causes us to be born of him and to live in him. In this inner prayer we can still meditate, but our attention is fixed on the Lord himself.
2710 The choice of the time and duration of the prayer arises from a determined will, revealing the secrets of the heart.
One does not undertake contemplative prayer only when one has the time: one makes time for the Lord, with the firm determination not to give up, no matter what trials and dryness one may encounter. One cannot always meditate, but one can always enter into inner prayer, independently of the conditions of health, work, or emotional state. The heart is the place of this quest and encounter, in poverty and in faith.
2711
Entering into contemplative prayer is like entering into the Eucharistic liturgy: we “gather up” the heart, recollect our whole being under the prompting of the Holy Spirit, abide in the dwelling place of the Lord which we are, awaken our faith in order to enter into the presence of him who awaits us. We let our masks fall and turn our hearts back to the Lord who loves us, so as to hand ourselves over to him as an offering to be purified and transformed.
2713 Contemplative prayer is the simplest expression of the mystery of prayer. It is a gift, a grace; it can be accepted only in humility and poverty. Contemplative prayer is a covenant relationship established by God within our hearts.9 Contemplative prayer is a communion in which the Holy Trinity conforms man, the image of God, “to his likeness.”
2715 Contemplation is a gaze of faith, fixed on Jesus. “I look at him and he looks at me”: this is what a certain peasant of Ars in the time of his holy curé used to say while praying before the tabernacle. This focus on Jesus is a renunciation of self. His gaze purifies our heart; the light of the countenance of Jesus illumines the eyes of our heart and teaches us to see everything in the light of his truth and his compassion for all men. Contemplation also turns its gaze on the mysteries of the life of Christ. Thus it learns the “interior knowledge of our Lord,” the more to love him and follow him.11
2717 Contemplative prayer is silence, the "symbol of the world to come"12 or "silent love."13 Words in this kind of prayer are not speeches; they are like kindling that feeds the fire of love. In this silence, unbearable to the “outer” man, the Father speaks to us his incarnate Word, who suffered, died, and rose; in this silence the Spirit of adoption enables us to share in the prayer of Jesus.
2718 Contemplative prayer is a union with the prayer of Christ insofar as it makes us participate in his mystery. The mystery of Christ is celebrated by the Church in the Eucharist, and the Holy Spirit makes it come alive in contemplative prayer so that our charity will manifest it in our acts.
Second, if you want an easy-to-read book on all forms of prayer, here’s one currently being used for intro prayer classes at the seminary my son attended. Written by a Jesuit and with imprimatur and nihil obstat, it has a Look Inside at amazon:
Armchair Mystic: Easing Into Contemplative PrayerApr 1, 2001
by Mark E. Thibodeaux S.J.
There are some good ideas about contemplative prayer from the others in this thread, but beware the topic of “contemplative prayer” sometimes seems to bring much “noise” as compared with “information.”