The new moon is the beginning of the lunar cycle, and means that the moon is completely in line with the sun and the Earth. We see a dark sky with no visible moon. It's a time of newness and rejuvenation. The new moon is the three days after the new face of the moon as well as the day of the new face of the moon.
Spells: New beginnings of any sort, beauty, health, personal improvement or new employment.
The waxing moon is the period of time between the new moon and the full moon. Every night, the moon gets a little larger. Any spell work that requires growth should be done now.
Spells: Courage, motivation, inspiration, friendship, elemental magick, healing or luck.
This is a time when the Moon is at its most powerful, and the magic most potent. Performing any positive spell at this time will achieve good results. Since the full moon only truly occurs for one night out of the entire lunar cycle, it can be hard to fit it into your schedule. You can harness the energy of the full moon for about 2 days before or after the night the moon is truly full.
Spells: Artistic projects, love, romance, fertility, psychic abilities or making decisions. Also healing, guidance, and completion spells.
The moon is waning as it gets smaller again, after the full moon. As the moon seems to disappear in the sky, use this time to do spell work to remove things from your life. The waning moon is a good time for the casting out of the old ways, banishing old habits, smoking, eating habits, the removal of troubles and worries.
Spells: Banishing bad habits, addictions, or ending relationships.
Typically, there is one full moon every month, but since the lunar cycle is a bit shorter than our calendar months, there is sometimes two. The second full moon in any given month is called a blue moon.
I want to mention the dark moon here, also called "The Dark of the Moon" because I find it very interesting personally. Many witches do not bother themselves with the dark moon or are not aware of the meaning of it. Below is a description of the dark moon.
Dark of the Moon - The Dark of the Moon (or dark moon) is traditionally the last three days of the lunar cycle, immediately preceding the new moon, and the time when the night sky is notably absent the presence of the Moon. Demetra George  notes that: 'The earliest peoples understood that the power of life lay in the darkness of the moon.' 'The purpose of the dark phase of any cycle is that of transition between the death of the old and the birth of the new. The dark time is a time of retreat, of healing, and of dreaming of the future.' i.e. the fallow times preceding outbursts of creativity and growth.
'Most of us do not realize we all have many dark phase times in our lives, and that these are naturally occurring periods in any life cycle. We fail to understand that endings are the precursors to new beginnings; thus when our life rhythms move us into and through these dark phases, we are ignorant of what is actually happening.'  It is the grandeur of Death and Rebirth, not merely an ending with the proverbial ride off into the sunset.
'The dark phase of the cyclical process is a phase of healing and renewal rather than one of fear and unknowing; a time of mystery, wisdom, and healing power -- all gifts of the Dark Moon Goddess.' 
'There is less energy available for outer activities and meeting the expectations of others, because the purpose of the dark phase is for focusing on the inner dimensions of our bodies and minds. If we can learn to attune ourselves to the natural rhythms of ebb and flow in our lives, we can use the intrinsic function of the dark times for healing and renewal. When we resist this inward motion in our psyche, then anxiety, stress, and fear are more likely to take hold of our emotions.' 
'The Triple Moon Goddess, in her new, full, and dark phases, was a model for the feminine nature in her entirety as maiden, mother, and crone. In her original worship the Dark Goddess, as the third aspect of this lunar trilogy, was honored, loved, and accepted for her wisdom and for her mystery teachings of renewal.' 
Spells: Healing, renewal, psychic spells. A good time to meditate on the inner self.
 Demetra George, Mysteries of the Dark Moon, The Healing Power of the Dark Goddess, Harper San Francisco, 1992.