Since the Moon's orbit around the Earth lies roughly on the same plane as the Earth's orbit around the Sun these can be illustrated on a flat sheet of paper.
Try drawing a small (1" or 3cm) circle in the center of a sheet of paper to designate the Sun.
Draw a large circle with the Sun at its center (a bit smaller than the width of the paper) to show the Earth's orbit around the Sun.
Draw a smaller circle (1/2" or 2cm) on the large circle you just drew to designate the Earth at some point in its orbit around the Sun. Shade the half of the Earth that is opposite the Sun.
Now draw a circle (2" or 5 cm) around the Earth to show the Moon's orbit around the Earth.
Using this as a template draw a small circle (1/4" or 1cm) on the Moon's orbit to show a possible position for the Moon and shade the half opposite the Sun.
Imagine how the Moon as illustrated in your drawing would appear from daytime (unshaded) and nighttime (shaded) places of the Earth's surface. Do the same for other positions of the Moon's orbit around the Earth.
Some times the Moon will be behind the Earth and so cannot be seen from half of the Earth's surface.
I hope this was fun but if you don't have paper and pencil
look here.