I believe that any endeavor should be tackled from process-orientation rather than outcome-orientation. While the goal is to achieve those moments of stillness, to achieve that outcome you can't focus on the outcome. Rather you need to focus on the process itself: breathing at a steady pace, being aware of any tension in body and feeling the sensation of being at ease in your body. When you're so focused on these things, the thoughts become softer and softer to the point of silence because you're so preoccupied with being present. Kind of like when you're in a heated discussion with a friend and you can't pay attention to anything else.