The Moon can be a powerful ally for Witches. As an ever changing, cyclic being, Her energies can be used for any type of magickal goal one can think of. All that's required to successfully work with Her is a little bit of background information, then there's no limit to the ways you can utilize Her power in your magick.
The Lunar Cycle is divided into four phases, both astronomically and astrologically. The cycle “begins” with the New Moon, a tiny crescent gleaming in the sky just as the Sun sets, first appearing 1-3 days after the Dark Moon. This is the start of the First Quarter. At this time the Moon is referred to as a Waxing Crescent. The Moon waxes on (grows in size/light) until the Second Quarter, about a week later, when She’ll be half up lit up, a half circle (in the Northern Hemisphere: light on the right side, dark on the left, in the Southern Hemisphere: light on the left side, dark on the right*.) From now till the Full Moon, She is called a Waxing Gibbous.
The Full Moon occurs about 2 weeks after the New Moon and is the end of the 2nd Quarter and the beginning of the 3rd Quarter Moon. The 3rd Quarter lasts until the Moon is again only half lit up in the sky, this time in the opposite direction, though (in the Northern Hemisphere: light on the left side, dark on the right, in the Southern Hemisphere: light on the right side, dark on the left;) this is the Waning Gibbous. Then, on till the Dark Moon, is the 4th Quarter Moon, the Waning Crescent.
Each phases lasts about 1 week, with the entire Lunar Cycle comprising, roughly, 28 days.
Magickally, we find that the energy of the Moon varies during each phase and thus can be used for different magickal purposes.
New Moon- new beginnings, great time to get started on long-term magick or spells that are cast over a period of time
Waxing Moon- as the Moon grows, so too does the amount of energy available: growth, expansion, increase, prosperity, fertility
Full Moon-the time of greatest power, a time of culmination and fruition: useful for healing, wishes, divination (especially scrying,) and strengthening your relationship with the Moon
Waning Moon- a time for decreasing magick: banishings, cleansings, purification, endings, protection
Dark Moon- a time of introspection and reflection, rest and preparation, a time for inner work: meditation, soul retrieval, astral travel, divination, Spirit communication
Acknowledging the Moon in all of Her phases will not only strengthen your connection with Her, thus making Her power more readily available to you, but it can foster a greater sense of balance and connection with all the Natural World.
* The different hemispheres see the Moon opposite (and upside down!) from each other's perspectives. In the Northern half, the light moves across the Moon from right to left, in the Southern half if moves from left to right.