This is a complex area and there are various views, esoteric concepts and a bit of marketing information thrown in. Even those interested in the highest good will want to bring others to their method which may have a religious component.
Both mind and body may relax. A human being can physically relax whilst manifesting an extreme fight-flight response. If you are in a life threatening situation a squirt of adrenaline may be very helpful, even life saving. But, in the practice of deep mental relaxation it is unhelpful. The reverse ie a swing from sympathetic into parasympathetic together with a reduction in mental activity is what is wanted. Clearly, zero mental activity cannot be achieved without death, however, one can drastically reduce mental activity whilst remaining awake and not asleep nor unconscious. In this state one dimly know one is awake. The mind is still with only this simple awareness. Afterwards, one is calmed and occasionally the calm is profound.
It is important to understand that this state of mental stillness can only be reached by deep mental relaxation. The use of mantras, breathing concentration and so on all involve mental activity and so the end state is "contaminated" by these things and the mind is not still.
The method I have summarized is that of the late eminent psychiatrist Dr Ainslie Meares who explains it in a couple of books (eg Ainslie Meares on Meditation). Meares believed that the still mind state that results from deep mental relaxation is probably not unlike that of our remote human ancestors. This deep mental relaxation is thus a normal human function, the minds own natural method of reducing tension, anxiety and fear which some people refer to as "stress".
In summary,
- sit in a chair, hands in lap.
- relax the body
- relax the mind
- effortlessly allow the relaxation to expand
- then the mind will slow and still - it feels like it is almost doing it by itself due to the effortlessness.
- practice is for about 10 mins or so twice a day (you can finetune later on).
- outside of meditation practice cultivate the feeling of calm and ease - Meares' referred to this feeling as the onward flow or onflow of meditation.
Some people are able to get the knack with just this little information but it will take longer than via a good set of instructions such as the book mentioned above. The books explains what to experience so you have a better idea and then the quality of practice is increased which shortens the learning time. A bit like physical training except the actual practice involves that effortlesness I mentioned. Those who try, strive, make, concentrate, focus and so on will find that the stillness eludes them.
Edit: Personally, I find this approach very helpful in recovery from physical training but that is minor compared to the benefits on many other aspects of living. Meares wrote it was a step towards a better life and I strongly agree on that point. In the area of still mind meditation the best way to know it is to experience it for yourself.