Some Cayce quotes to get you started:
For all prayer is answered. Don't tell God how to answer it. (4028-1)
For prayer is supplication for direction, for understanding. Meditation is listening to the Divine within. (1861-19)
Then set definite periods for prayer; set definite periods for meditation. Know the difference between each. Prayer, in short, is appealing to the divine within self, the divine from without self, and meditation is keeping still in body, in mind, in heart, listening, listening to the voice of thy Maker. (5368-1)
What IS Meditation? It is not musing, not daydreaming; but as ye find your bodies made up of the physical, mental and spiritual, it is the attuning of the mental body and the physical body to its spiritual source. Many say that ye have no consciousness of having a soul, - yet the very fact that ye hope, that ye have a desire for better things, the very fact that ye are able to be sorry or glad, indicates an activity of the mind that takes hold upon something that is not temporal in its nature, - something that passeth not away with the last breath that is drawn but that takes hold upon the very sources of its beginning - the SOUL, - that which was made in the image of thy Maker - not thy body, no, - not thy mind, but thy SOUL was in the image of thy Creator. Then, it is the attuning of thy physical and mental attributes seeking to know the relationships to the Maker. THAT is true meditation. (281-41)
MEDITATION is EMPTYING self of all that hinders the creative forces from rising along the natural channels of the physical man to be disseminated through those centers and sources that create the activities of the physical, the mental, the spiritual man; properly done must make one STRONGER mentally, physically, for has it not been given? He went in the strength of that meat received for many days? Was it not given by Him who has shown us the Way, "I have had meat that ye know not of"? As we give out, so does the WHOLE of man - physically and mentally become depleted, yet in entering into the silence, entering into the silence in meditation, with a clean hand, a clean body, a clean mind, we may receive that strength and power that fits each individual, each soul, for a greater activity in this material world. (281-13)
Depend more upon the intuitive forces from within and not harken so much to that of outside influences - but learn to listen to that still small voice from within, remembering as the lesson as was given, not in the storm, the lightning, nor in any of the loud noises as are made to attract man, but rather in the still small voice from within does the impelling influence come to life in an individual that gives for that which must be the basis of human endeavor ... (239-1)