Probably there is no astronomical subject that has been more generally misunderstood than that of solar and lunar eclipses. It is well to remember that solar eclipses can only occur at time of new moon and lunar eclipses only at the time of full moon; and at the time of eclipses, whether lunar or solar, the moon is at or near its nodes, the points where its orbit crosses the ecliptic. There are always at least two solar eclipses every year and there may be as many as five. There are years when there are no lunar eclipses, though ordinarily both solar and lunar eclipses occur every year, some partial others total.
The moon shines only by reflected sunlight. It is of itself a solid, dark body with its day surface intensely hot and its night surface intensely cold, a world of extreme temperatures.
At new moon all of the night side of the moon is turned toward us, at full moon all of the day side. At other phases we see part of the day side and part of the night side and the illuminated side of the moon is always the side that is towards the sun. Failure to observe this simple rule leads to many grievous blunders in depicting the moon.
At the time of new moon the moon, moving continually eastward, passes north or south of the sun from west to east except when it passes directly in front of the sun, causing eclipses. A day or so later the waxing crescent moon or the "new moon," as it is popularly called, becomes visible low in the west immediately after sunset. The moon is now east of the sun and will remain east of the sun until the time of full moon. During the period from new moon to full moon it will, therefore, rise after the sun and set after the sun. The waxing crescent moon will not be visible in the morning hours because, inasmuch as it rises after the sun, it is lost to view in the sun's brilliant rays. Nevertheless, it follows the sun across the sky and becomes visible in the west as soon as the sun has disappeared below the western horizon. The thin illuminated crescent has its horns or cusps turned _away_ from the point where the sun has set. The horns of the crescent can never point _toward_ the horizon since the illuminated side of the moon is always turned toward the sun whether the sun is above or below our horizon.