The moon is a powerful tool to use in Witchcraft.   Each phase of the moon has its own power, and if we perform spells or rituals to coincide with the phase of the moon, our magick will be stronger.  Also, for many Witches, the Moon is a representation of the Goddess. An Esbat is a Pagan celebration that is held at any time other than a Sabbat.  Esbats are commonly held on the Full Moon, however some Pagans hold rituals to honour all phases of the Moon. You can chose to celebrate the Full moons only, the Dark moon only, the Full Moons and Dark Moons, or the Full, Dark and the Quarter Moons.   There are no rules about which phases you celebrate, you may chose not to celebrate any of the moon phases and only use their powers to aid your spells.

The top line shows the moon moving from Full to the First Quarter through to the Dark moon.  The next line shows the Dark Moon travelling to the Last quarter and back to the Full moon. In the Northern Hemisphere the phases occur at the same time, but they see a mirrored image of the Moon.  So their First Quarter looks like our Last Quarter etc.
 

In most Pagan traditions the moon symbolises the Goddess, while the Sun symbolises the God.  The Goddess rules over night time and the God over day time.  The moon phases reflect the changing aspects of the Goddess.  The New moon represents the Maiden, the Full moon represents the Mother, the Dark moon represents the Crone.  Some people use a 5 phase cycle.  With the 5 phases they would then go like this:  The New Moon represents the Maiden, the Waxing phase/First Quarter represents the Enchantress, the Full Moon represents the Mother, the Waning phase/Last Quarter represents the Grandmother, the Dark Moon represents the Crone.  Some people use other Goddess phases for the Moon phases, but these are the most common two. 
 

Moon Goddesses
Aega (Greek), Anna Perenna (Roman), Andromeda (Greek), Anu (Irish), Aponibolinayen (Philippino), Aradia (Roman), Arianrhod (Welsh), Artemis (Greek), Athtor (Egyptian), Belili (Middle Eastern), Callisto (Greek), Cerridwen (Celtic), Coalicue (Aztec), Delia (Greek), Diana (Greek), Eithne (Irish), Epona (Gaulish-Celtic), Freya (Norse), Hecate (Greek), Ida (Aryan), Inanna (Sumerian), Ishtar (Babylonian), Isis (Egyptian), Kuan Yin (Chinese), Lucina (Roman), Luna (Roman), Mari (Basque), The Morrigan (Celtic), Nina (Sumerian), Rhiannon (Welsh, Cornish), Sefkhet (Egyptian), Selene (Greek), Titania (Roman)

If you wish, you could also think of a Triple aspect of a God to balance the Full Moon worship. New Moon represents the Young hunter, the Full Moon represents the Father, the Dark Moon represents the wise Sage/Grandfather.  When performing a Moon ritual it is not necessary to invoke the God if you do not wish to, but you can invoke a Moon God if you like.  
 

Moon Gods
Nanna (Sumerian), Deert (Aboriginal), Khons (Egyptian), Thoth (Egyptian), Chons (Egyptian), Alignak (Inuit), Chandra (Aryan), Eterah (Semitic), Fati (Polynesian), God D (Myan), Gou (Benin), Hermes (Greek), Jacy (Native South American), Samas (Semitic), Ilmaquh (Middle East), Mani (Nordic), Itzamna (Mayan), Menu (Lithuanian), Pandion (Greek), Sin (Assyrian), Soma (Aryan), Taukiyomi (Japanese), Tsuki Yomi (Japanese), Varuna (Hindu)

The Full moon: The power of the Full moon lasts from 3 days before the Full moon, the day of the full moon, and the 3 days after the full moon.  The power is strongest at the point the full Moon, which can happen during the day. All works of Magick are best performed on a Full Moon. As it is the most powerful Moon phase.

Goddess Aspect: Mother
Associated Goddesses: Full Moon or Mother Goddesses, such as: Danu, Cerridwen,
Gaia, Aphrodite, Isis, Artemis, Anna Perenna, Ariel, Venus, Inanna, Luna, Selene.
Powers:  All works of magick can be performed on a Full Moon.

A full moon is a great time to charge items you will be using in rituals or spells.  You can leave them under moonlight over the 3 days of the Full moon to imbue them with her power and blessing.  You can also make holy water during a Full moon, and save it for use in rituals throughout the rest of the month.

Goddess aspect:  Crone
Associated Goddesses:  Dark Moon and Crone Goddesses, such as Hecate and Cerridwen.
Powers: Some people say that no magick should be performed on the actual day of the Dark moon, although the banishing powers of the moon may be used on the 3 days before and the 3 days after the Dark moon if you wish.  Other people say that the Dark moon is a time of protection, both physical and spiritual, and it is the most powerful time to banish negativity, or banish that which we no longer need such as addictions.   Whether you cast spells on a Dark Moon is up to you, do whatever feels right for you

Associated Goddesses:  Virgin or Maiden Goddesses such as Anu, Artemis, Juno, Titania, White Shell Woman, Aphrodite, Diana.
Powers: New Beginnings, healing, beauty, self-improvement, garden magick, job hunting, love and romance, networking etc.

Goddess Aspect: Maiden
Associated Goddesses: Maiden Goddesses such as: Artemis, Branwen, Eriu, Nymph, Epona, Diana, Yemanja,
Powers: Psychic enhancement, abundance, new projects, growth, expansion, attraction, increasing health and well-being, love, knowledge,  spirituality, fertility, friendship, inspiration, energy, vitality, freedom,  luck etc.

Goddess Aspect: Crone
Associated Goddesses: Crone Goddesses such as: Callieach, Banshee, Hecate, Kali, Morrigan, Cerridwen,
Powers: Reversing spells, banishing negative thoughts, letting go of the past, guilt, weight loss, releasing anger etc.

The First Quarter: This occurs 7 days after the New Moon.  This is the middle and most powerful point of the Waxing phase of the Moon.  So the powers of the Waxing phase apply.

Spells to begin increase, protection for animals, bring change, help with business affairs.
 

Gibbous Moon:
10 to 13 days after the new moon

Spells for great increase, grant patience, growth, harmony
Timing: It's a wonderful time for working around 10:00 to 11:00 p.m.
 

Waning Gibbous:
Night after the full moon to 7 days after the full moon

Spells that diminish Addictions, stress, help through divorce, or to cut a line to your ex.
 

Waning Crescent
7 days after the Full Moon to the New Moon

Spells that greatly diminish Obstacles, fights/arguments, pain, to stop a criminal
Try to remember that each of the 4 phases (Full Moon, New Moon, Waxing Moon, Waning Moon) consists of 7 'working' days for a total of 28 days in a lunar month. Each group of seven 'working' days are days considered generally appropriate for work under the influence of that particular moon phase. These are general magickal times, not actual times.

The lunar phase is important in determining the best time for magick. There are basically two lunar phases: waxing moon (ideal time for positive magick) and waning moon (ideal time for banishing/negative magick, study, and meditation). In between you'll have the dark moon (the time of greatest power for banishing and negative magick) and the full moon (the time of greatest power for positive magick).
 

Lunar Eclipses

Eclipses represent the union of the Sun and the Moon, and thus are very powerful.  Any type of magick is enhanced by performing it on an eclipse.
 

Moon Void of Course

The moon is void of course the day before it enters a new moon sign , Some say you should avoid doing any important magickal workings while the moon is void of course. (of course, if you have to, then you can)  You can also use the moon signs properties to add to your magickal workings

Names for the Moons:

January: Wolf moon
February: Storm moon
March: Chaste moon
April: Seed moon
May: Hare moon
June: Dyad (pair) moon
July: Mead moon
August: Wyrt (green plant) moon
September: Barley moon
October: Blood moon
November: Snow moon
December: Oak moon

Blue Moon-Second full moon in month
Harvest Moon-Full moon nearest Mabon