This is what you are to do. Lift your heart up to the Lord with a gentle stirring of love, desiring him for his own sake and not for his gifts. --The Cloud of Unknowing, Chapter 3
In the 1970s, drawing from The Cloud of Unknowing and other Christian mystical writings, three Trappist monks--William Meninger, Basil Pennington, and Thomas Keating--developed a simple method of silent prayer. This method came to be known as Centering Prayer, referencing Thomas Merton's definition of contemplation as prayer "centered entirely on the presence of God." (You can learn more about Centering Prayer through Contemplative Outreach.)
Centering Prayer is simply sitting in silence, open to God's love and your love for God. This prayer is beyond thoughts, emotions, or sensations. Like being with a very close friend or lover, where words are not required, Centering Prayer brings your relationship with God to a level deeper than conversation, to pure communion.
Because our minds are so attached to thinking, Father Thomas Keating sometimes suggests choosing a sacred word, with one or two syllables, "as the symbol of your intention to consent to God's presence and action within. [Then,] sitting comfortably and with eyes closed, settle briefly, and silently introduce your sacred word. . . . When you become aware of thoughts, return ever-so-gently to your sacred word. At the end of the prayer period, remain in silence with eyes closed for a couple of minutes." 
Two sessions of 20-30 minutes of Centering prayer is recommended each day, but if that is too much for you, begin with five or ten minutes. Let go of all expectations or goals during this time. It is not about achieving anything, whether emptying your mind or finding peace or achieving a spiritual experience. There is no way to succeed at Centering Prayer, except to return again and again to love. Allow thoughts to come and go without latching onto them, without judgment. "Ever-so-gently" bring your sacred word, the symbol of your intention, back to mind and return to resting in Presence.