Lunar Cycle
The moon is only visible when the sun illuminates its surface. During the 29-day lunar cycle, the moon's visibility ranges from the invisible new moon to the bright full moon. During a new moon, the moon rests between the Earth and the sun. All of the sun's illumination hits the back of the moon and no illumination hits the front of the moon. As the moon revolves around the Earth, the sun's illumination hits a greater and greater part of the moon. A full moon occurs when the moon is behind the Earth and the sun hits both the Earth and the moon.
Afternoon
The moon never disappears from the sky. During most days, however, the sun creates an environment too bright for lunar visibility. But when the moon rests in a particularly bright version of the sky, it becomes visible. Typically, the moon is visible in the afternoon during the waning gibbous phase, a phase of the lunar cycle where the moon rises during the late evening and sets in the late morning.
Morning
During the early morning, only a fraction of the sun's light hits the Earth. Because the sky lacks its usual brightness, the light of the moon is often visible. Typically, the early morning moon appears during a waxing gibbous or waning gibbous phase. After a full moon, the moon rises and sets at a later time each night. The moon also becomes less and less visible, however, as the lunar cycle progresses, due to the moon's position in relation to the sun.
Moon Viewing
Though the moon's phases offer a predictable pattern of rising in the evening and setting in the morning, the exact time of the moon's visibility varies during different times of year. If you want to view the morning or daytime moon, consult a lunar calendar. Lunar calendars list the exact time when the moon becomes visible. Typically, the daytime moon is most visible on cloudless days with low humidity.