The Moon may not be visible during the day of the New Moon, when it is in the sky during the daytime. The side facing Earth will be almost totally non-illuminated because the Moon is between the Sun and the Earth. However, it may be visible shortly before sunrise or shortly after sunset as a very narrow crescent.
You can see the moon sometimes
The moon
You see just that part of the moon that the sun is shinning on.
Sometimes!
Sometimes the brightness of the light from the moon drowns out the star's light.
the moon is in the opposite of the sun
You can't see the moon during the 12 to 30 hours before and after the New Moon. So that's anywhere from 1 to 2-1/2 days during the month, depending on the exact angle of the ecliptic to the horizon, and the moon's orbital inclination relative to the ecliptic. (Those things change from month to month.)
sometimes clouds may block your view of the moon
The apparent wobbling by the Moon is called "libration"; you can find more information, for example, in the Wikipedia article on "Libration". The Moon doesn't really wobble; rather, from Earth we sometimes see different parts of the Moon, because (a) sometimes we see it more from the north, sometimes more from the south (since the Moon's axis is not exactly perpendicular to its orbit around Earth), and (b) since the Moon's orbit isn't exactly circular, but it rotates at a constant angular speed, as a result we sometimes see a bit more of the Moon's east side, and sometimes more of its western side. In total, we can see about 59% of the Moon's surface from Earth (at different times).
In the sky, you can see clouds, the sun, the moon, stars, and sometimes airplanes.
the reason we sometimes don't see the moon is because the sun is in a posision where the light doesn't reach the moon, there for the light isn't reflected to Earth and we can't see it.
there are phases of the moon because when it orbits us sometimes you can't see it and other times you can see half it all depends.