Someone asked me recently "what is the Prayer of the Quiet?"
I just found a super, clear answer from St. Teresa Benedicta of the Cross (aka Edith Stein)
"Prayer is the communion of the soul with God. God is love, and love is goodness giving itself away. It is a fullness of being that does not want to remain enclosed in itself, but rather to share itself with others, to give itself to them, and to make them happy. All creation exists thanks to this divine love spending itself. However, the highest of all creatures are those endowed with spirit, able to receive God's love with understanding and to return it freely; angels and human souls. Prayer is the highest achievement of which the human spirit is capable. But it is not merely a human achievement. Prayer is a Jacob's ladder on which the human spirit ascends to God and God's grace descends to people. The stages of prayer are distinguished according to the measure in which the natural efforts of the soul and God's grace participate. When the soul is no longer active by virtue of its own efforts, but is simply a receptacle for grace, one speaks of a mystical life of prayer.
So-called vocal prayer is designated as the lowest stage, prayer remains within specifically designated spoken forms: the Our Father, the Hail Mary, the rosary, the Divine Office. . .
Meditative Prayer is one stage higher. Here the spirit moves freely without being bound to specific words. It immerses itself, in the mystery of the birth of Jesus. The spirit's imagination transport it to the grotto in Bethlehem, seeing the child in the manger, the holy parents, the shepherds and the kings. The intellect ponders teh greatness of divine mercy, and the emotions are seized by love and thankfulness, the will decides to make itself more worthy of divine love. This is how mediative prayer involves all the soul's power and, when practiced with faithful persistence, can gradually remake the whole person. However, the Lord has yet another way of rewarding fidelity in meditation; by elevation to a higher manner of praying.
St. Teresa calls the next stage the prayer of quiet or simplicity. Various activities are replace by a recollection of spiritual energies. The soul is no longer in a position to reflect intellectually or make definite decisions; she is completely engaged by something she cannon avoid, the presence of God who is close to her and allows her to rest in him. While the lower prayer stages are accessible to every believer by human effort, albeit aided by the grace of God, we are now standing at the border of the mystical life of grace that cannot be entered by virtue of human energy, for here only God's special favor grants admission."
Love for Love: The Life and Works of St. Teresa of Avila by St. Teresa Benedicta of the Cross, Part 1, Carmel Clarion April-June 2010 pg 10-11.
In a simple summary, in prayer of the quiet we "recollect ourselves" -we try to keep our mind still and silent- and then we let God do the rest.