Rules for meditation: There is a basic technique called Vipassana (Pali, “insight”) which comes from the oldest tradition of Buddhism. The advantage of this method is can be taught in a completely secular way.
The quality of mind cultivated in Vispassana is generally called mindfulness and there is a growing literature on its psychological benefits. Mindfulness is, simply put, a state of open non-judgemental, and non-discursive attention to the contents of conciousness whether pleasant or unpleasant.
Cultivating mindfulness has been shown to modulate pain, mitigate anxiety and depression, improve cognitive function (although exercise is far more effective as method in that regard) and even produce changes in brain matter density in areas of the brain related to learning, memory, emotional regulation and self awareness.