Since the Moon shines only by reflected sunlight, only part of it is lit at any one time -- that part which is turned toward the Sun. As it moves around the Earth, we see it from different perspectives, hence its phases.
The full moon is the very worst time to observe it. This is because sunlight is coming straight down onto the Moon's surface, and the mountains and crater walls cast almost no shadows. Everything will seem to be a jumble and features will be hard to recognize. A better time to observe the Moon is when it is a crescent or half.
The Moon is up during the daytime as much as during the night, so you will need to know what phase the Moon is in to determine if you can see it tonight. Most calendars have a little diagram to show the Moon phases. A full moon will rise around sunset. A first quarter moon will rise around noon, and a last quarter moon around midnight. The Moon rises about an hour later each day than it did the day before, so you can usually figure out when it should be popping up. And, of course, the Moon rises in the east just like the Sun does (you know why, right?).
First, look at the Moon with your naked eye. Do you see the large dark patches or splotches? These dark patches remind some cultures of a human face, others of a rabbit, or girl carrying water buckets, or a dragon. The patches are lava flows from ancient underground volcanoes. Galileo and early observers thought they might be seas, so named them Maria, the Italian word for ocean. But there has never been any water on the Moon.
Now point your telescope toward the Moon. You'll see that it's crowded with detail -- mountains, hills, valleys, ridges, lava beds, and thousands of craters. The craters are everywhere, clustered thickly, many on top of each other, some in pairs or complicated groups. Many have rays of ejected material, spewn out when the meteor hit. The largest craters are over 160 km (100 miles) in diameter. Most of these craters date from the time the Moon was young, about 3.5 billions years ago.
Look first along the "terminator", or boundary between the sunlit and dark hemispheres, where the Sun is just rising or setting over that area of the Moon. The craters will look splendid, with dark shadows thrown across their floors. Try to sketch one or two of the best ones. Then observe these same craters several nights in a row, and you'll find their appearance alters, sometimes dramatically, as the angle of sunlight changes.
It is relatively easy to keep track of the craters on the Moon because they always stay in the same place each night (do you know why?) . A good way to begin observing the Moon is to make an outline map then sketch a few of the craters which are most visible. Make observations for several nights, adapting your sketches as you see new detail. Here are 4 craters which you might start with:
Tycho - Look for Tycho in the southern uplands (mountains), #2 on the map. Tycho is the largest, most dramatic crater, with huge ray systems radiating from it. There are many minor ray centers as well. Tycho is about 87 km (54 miles) in diameter.
Copernicus - Copernicus is another dramatic crater, lying slightly north of the Moon's equator (#4 on the map). Like Tycho, it also has prominent ray systems radiating from it.
Plato - Plato is a very dark dot on the edge of the Sea of Showers (Mare Frigoris)
about in the center of the upper quarter of the Moon (#8 on the map). It has a more or less level floor, and is so dark grey in color that it's always easy to locate. Plato is about 100 km (60 miles) in diameter.
Aristarchus - look for bright Aristarchus on the grey plain in the upper left quadrant (#6 on the map). It has brilliant walls and a central mountain. Although it's only 37 km (23 miles) in diameter, it's easy to find when it's lit by the Sun. It can even be seen on the night side of the Moon, by light reflected onto the Moon from the Earth, an effect nearly always visible when the Moon is a slender crescent.


Sketch how you see the moon here. Specifically look for Aristarchus, Plato, Tycho, and Copernicus.