The fastest way to determine the current moon phase for the night is to check a moon phase calendar. The website space.com keeps an accurate moon calendar through the end of the year, and a separate section of the site tracks the current phase of the moon on a daily basis. Its calendar includes definitions of all phases of the moon and other interesting dates related to moon-watching.
The current phase of the moon depends on how much of the side of the moon facing the earth is illuminated by the sun. The first phase, called a new moon, occurs when the side of the moon facing earth receives no sunlight. The moon is referred to as waxing while it increases in illumination, moving through the phases of crescent, quarter, gibbous and finally full. As the moon's illumination decreases, it becomes a waning moon, going though gibbous, quarter and crescent phases until it returns to the new moon phase. It takes 27.3 days for the moon to move through all of its phases, with each phase occurring approximately a week apart.
Space.com's moon phases calendar also includes editor's notes marking some other interesting astronomical phenomena related to the moon. This includes solar eclipses, when the moon passes directly in front of the sun instead of above or below it; and lunar eclipses, when the earth passes between the sun and the moon and the earth's shadow is visible on the earth's face. Dates of supermoons are also included; these are moons that look larger and brighter than average.