The saints have pointed out the scriptures that best describe the experience of contemplative prayer. "Be still and acknowledge that I am God, supreme over nations, supreme over the world" (Psalm 46:10). Contemplative prayer is a gaze of faith, fixed upon Jesus. As a parishioner told the Cure of Ars, "I look at Him and He looks at me" (Catechism of the Catholic Church #2715).
Contemplative prayer could last a moment - it could last several hours. A person realized that he has experienced it afterwards, as he realizes that he has changed. The psalms sing to his soul: "My whole being yearns and pines for Yahweh's courts, My heart and my body cry out for joy to the living God" (Psalm 84:2). He realizes that he is in love with God!
See Thomas Dubay, Fire Within (San Francisco: Ignatius Press, 1989) page 65-69. Also see Elizabeth of the Trinity, Heaven in Faith and also Last Retreat, for an explanation of scripture as it relates to contemplative prayer. These can be found in Elizabeth of the Trinity, The Complete Works, trans. Aletheia Kane, O.C.D., Volume One (Washington DC: ICS Publications, 1984) all pages.