To get started, he suggests creating a favorable environment to make it easier to practice. There should be a sacredness about one’s place of meditation. Mindfulness meditation is best undertaken in a place of silence that is not too disturbing. Some people create special alcoves in the home with candles, plants, yoga mats and fountains, where they can be at peace to meditate each day. Others retreat to their gardens, an uplifting place of respite. Another group of people prefer the company of other like-minded individuals at a special meditation center.
In that comfortable place, one should begin mindfulness meditation with the proper posture. It seems that lying down would be the most comfortable position, but that is not how meditation works. A meditation teacher will instead instruct pupils to sit upright, with hands resting palm-down on the thighs and hips straight. Some people who meditate sit on a zafu or gomden cushion on the floor, with their legs crossed. Others prefer to sit upright in a chair, with their feet touching the ground. “The energy flows better when the body is erect,” explains Sakyong Mipham Rinpoche, “and when it’s bent, the flow is changed and that directly affects your thought process.” This posture will help meditation pupils remain awake, even though they are very calm.
The above excerpt is from a little article entitled simply "Mindfulness Meditation: Let Go of Your Thoughts" .