The Quarters & Phases
Each month, the Moon waxes and wanes through a period of approximately 29 1/2 days. The waxing moon phase, from New Moon to Full Moon, lasts approximately two weeks. The waning phase, from Full Moon to New Moon, also lasts two weeks. The turning of the moon is further broken down into four parts, called quarters. Each of these four phases has a first half and second half, ultimately breaking the moon's cycle into eight equal parts.
The NEW MOON and FIRST QUARTER make up the WAXING PHASE
At the NEW MOON, the Sun and Moon are in the same place relative to Earth, or conjunct. The Moon is between the Sun and the Earth and thereby reflects no light visible from Earth. The Moon is not visible at first, since it rises at the same time as the Sun. The last half of this quarter is called the Crescent Moon (four days into the lunar cycle).
The FIRST QUARTER begins halfway between the New Moon and the Full Moon, when the Sun and Moon are at right angles. This Half Moon rises about noon and sets around midnight. It can be seen in the western sky during the first half of the night. The last half of this quarter is called the Gibbous Moon (3 1/2 days until fullness).
The FULL MOON and LAST QUARTER make up the WANING PHASE
The FULL MOON occurs when the Sun and Moon are opposite one another and the Earth between them. From our vantage point here on Earth, we can see the full reflection of the Sun's rays on the Moon. The Moon can be seen rising in the east at sunset, rising afterwards a little later each evening. The last half of this quarter is known as the Disseminating Moon (3 1/2 days past full).
The LAST QUARTER begins about halfway between the Full Moon and the New Moon, when the Sun and Moon are at 90 degrees. This decreasing moon rises at midnight, and can be seen in the east during the last half of the night, reaching the overhead position just about as the Sun rises. The last half of this cycle is called the Balsamic Moon (three or four days before total darkness).
For a list of correspondences for the eight phases of the moon, go here.