A New Moon happens when the Moon is conjunct the Sun (0°). It is the starting point of the 29-day lunar cycle.
It is often a time of low energy, when it seems to go underground or unconscious. For 1-3 days before and after a New Moon, we may feel tired, mellow, lethargic, meditative or a bit depressed.
Starting at the New Moon, we may see themes, events, feelings or urges starting to emerge that develop and become clarified around the Full Moon.
At the New Moon we can't see the Moon because it's too close to the Sun and drowned out by its rays. As the Moon moves past the Sun, we begin to see the sliver of the Crescent Moon -- how soon after the exact New Moon depends on several factors, but it can usually be seen with the naked eye (weather willing) within about 24 hours. Watch for it just after sunset near the western horizon.
In the 2 weeks following the New Moon, we see an increasing amount of light in the Moon from a Crescent Moon to the Full Moon, when the entire face of the Moon is brightly visible. We call this a Waxing Moon, and astrologically it is associated with gradually building and increasing energy.
After the Full Moon, the size of the Moon's light gradually decreases over the next 2 weeks. Called a Waning Moon, it is associated with being a time of dissipating and disseminating energy.
A New Moon can also be a Solar Eclipse. This typically happens twice per year, about 5-6 months apart, and occurs when the Sun and Moon are both conjunct and parallel, and within about 18° of the Lunar Nodes axis.
Related articles: Sun and Moon ~ The Lunar Cycles and Blue Moon Lunacy.