Mindfulness meditation is an entirely secular practice. Experts in this practice generally acquire their training in a Buddhist context where it is known as vipassana (Pali, “insight”) meditation. Unlike most other forms of “spiritual” instruction, this method of introspection is simply a state of  clear, nonjudgmental, and nondiscursive attention to the contents of consciousness (yours). There is evidence that cultivating this quality of mind can modulate pain, mitigate anxiety and depression, improve cognitive function, and even produce changes in gray matter density in regions of the brain related to learning and memory, emotional regulation, and self awareness.

The practice of mindfulness is extraordinarily simple to describe, as is tightrope walking:

1. Find a horizontal cable that can support your weight. (When not asleep, find a mind.)
2. Stand on one end. (Note what is.)
3. Step forward by placing one foot directly in front of the other. (Remain present.)
4. Repeat. (Note what is.)
5. Don’t fall. (Don't lapse into inner monologue.)

But neither practice is easy. Clearly, steps 3-5 entail practice. Happily, the benefits of training in mindfulness arrive long before mastery ever does, and falling occurs almost ceaselessly, every moment that one becomes lost in thought. The problem is not thoughts per se but the state of thinking without knowing that one is thinking.

Thought is not mindfulness. When thought takes over, note the fact and return to here-and-now attention. Human minds are so habituated to incessant chatter that initially taking even a moment's break is a challenge. Beginners often must resort to paying such attention as they can muster to simply following their breathing until they can simply witness all objects of consciousness—sights, sounds, sensations, emotions, and even thoughts themselves—as they arise and pass away. Mindfulness practice has nothing to do with believing or not believing anything.

 

The above was adapted from: http://www.samharris.org/blog/item/how-to-meditate where details abound.