The New Moon, is when the moon has just made it's appearance at the sky and is used to cast spells about new beginnins and things you want to grow in time.
The Waxing Moon, is when the moon is getting bigger and it is used to cast spells in order to attract things to your life.
The Full Moon, is when the moon is at it's fullest and has it's full power on. It's a neutral phase for me but i'd rarely recommend casting any kind of hex on it. It's power last 3 days the day of the full moon, the day before and the day after.
The Waning Moon, is when the moon is getting smaller and it is used to cast spells that will banish things out of your life,cleansings and also hexes.
The Dark Moon, is when the moon isn't visible at all at the sky and it's the perfect time to do cardcore banishing,cleansing and some really nasty hexes. The Dark Moon is sacred to the goddess Hekate.