new moon: the moon is literally new. a rebirth. use this moon for intentions to do with fresh beginnings, starting again, cleansing.
waxing moons: the moon is increasing its size, it is opening; use these moons for intentions about gaining, growing or expanding.
full moon: the moon is at full charge, and can be the most powerful phase in the moon cycle. use this moon for intentions to do with power, clarity, or psychic ability.
waning moons: the moon is decreasing its size, it is closing; use these moons for intentions about ridding yourself of something (or someone).
application to the craft:
focus is the most important aspect of bringing an intent to manifest itself. focusing your energy can be made simpler by working with a compatible energy in the world as you focus that intent.
if the world around you is releasing an energy complementary to yours, it can be easier for that energy to find its way into reality; as opposed to facing any natural adversity.
cast soft energy intents in soft phases of the moon. (tranquility, creativity)
cast hard energy intents in hard phases of the moon. (strength, control)
this, in my opinion, is the concept of “the power of thought.” when more than one person thinks a thought, that thought holds more weight. this could explain why people practicing or praying together can often yield stronger, or more immediate results. it is a similar reasoning as incorporating tools and ritual into magick, as well.
your energy is a power in itself. but using the power of the elements, the environments, and the world can serve to add to that power.