Astrologers usually advise people not to start important new projects in the last three days of the Moon cycle; before the New Moon. This is a time to plan but not to instigate. For example, if you start a new job in the last three days of the old Moon, it probably won't last. It will fall apart in some way. If you plant some flowers or vegetables just before the New Moon, they are less likely to survive or thrive.
The Moon has a 28 day cycle through the zodiac. It spends about two and a half days in each sign every month. The Full Moon occurs fourteen days after the New moon.
Isabel Hickey sums it up well in her classic book;
"Nature has an ebb and a flow like the tides in the ocean. The tides can be used or neglected. Everything in nature is on the upswing between the New and Full Moon; when its energy starts to recede and is ebbing, the tide is at its greatest passivity before the New Moon. Note the lack of pep and vitality in people in the last phases of the dying Moon."
Update 2006: To see the schedule for New Moons this year check out the moon cycles for 2006 at AstroProfile.com.
The above fine art print is "Moon, Persimmon & Moth" by Anita Munman