A cresent moon precedes and follows a new moon. The moon goes through the phases new, waxing crescent, first quarter,waxing gibbous, full, waning gibbous, last quarter, waning crescent, and back to new. Each lunation, or cycle of the moon, takes around 29.5 days. Thus a waxing crescent follows the new moon, and a waning crescent precedes the new moon.
For images of the phases, check out this web site at the U.S. Naval Observatory. The movie also shows the lunar libration, where the angle at which we view the moon changes slightly.