An apparently simple pose...after all who doesn't know how to lie down and chill out?
But it is the core practice of Yoga, for it is the complete stilling of the body, which allows the relaxation of the entire psycho-physiological system, and thereafter the cessation of identification with the body, as the senses are withdrawn (pratyahara).
Yoga is the balancing of the two halves, the sun and moon, Ha + Tha, right and left sides of brain, the ida and pingala, the yin and yang, and at the body level it includes learning to switch between the sympathetic and parasympathetic nervous systems. To flow with an activity while we do it and to detach completely (letting it drop absolutely) when we are not doing it. Shavasana is the training ground for this.
Lie on your back. Spine, neck and head are in a straight line. Feet are hip distance apart and falling out towards sides. Arms are down alongside body and a little away from body. Palms of the hands are facing upwards or slightly inwards so that there is no contact between the finger-tips and the floor. The eyes and mouth are gently closed, and the chin is slightly tucked towards the chest so as to elongate the back of the neck (comfortably).
Settle the body, and then let the weight of the body drop towards the floor. With each exhalation more of the weight of the body drops towards the floor. Allow the body to become completely still and only move if you absolutely have to.
Allow the natural breath to become rhythmic and relaxed, and without changing that breath in any way, count the breaths backwards for some time, from 27 to 1. Repeat as necessary.
Or you may repeat a mantra on the breath or in rhythm with the heartbeat.
Or you may move the mind through a rotation of consciousness of the body parts, becoming aware of the different parts and letting go more deeply there.
But it is not a time for getting lost in thoughts.
If you have a bad back at the moment, bend your knees and place your foot-soles on the floor (hip distance apart). You could have pillow between knees here, and let knees fall in towards each other.
A more actively releasing Shavasana is one developed by Jana Dixon (http://biologyofkundalini.com/) to release in the heart-space or where the diaphragm has become restricted due to emotional stress. Here you put a raised cushion/blankets under the back at level of diaphragm (just below shoulder blades) and open arms out more to sides, and let head rest back....Adjust the level of the cushion/blanket so that it accommodates your comfort and purpose.
Here is a Shavasana practice as taught by Swami Pragyamurti.