One of the very first celestial objects most amatuer astronomers observe is the Moon. At only 240,000 miles, the Moon has been a focal point of man from the beginning of recorded history. The Moon formed about 4.5 billion years ago. Earlier in its lifetime the Moon was bomb-barded with left over remnants of our solar system. Without an atmosphere, no weathering has taken place. All geologic features remain frozen in time, some 3 ½ mil.years old.
Because the moon is so close to us, even a small telescope can show a wealth of detail. Using a 70mm (3") at about 100x, just about all the features of the lunar surface can be brought into view. A 3" should be able to see features one mile in diameter. A 10" can spot features the size of football field.
To really see great features observe the moon during crescent phases. Catching mountain tops protruding high enough to catch the sunlight while being surrounded by dark lower terrain is breathtaking. On the floor of large craters, follow the "wall shadows". The sides of the craters can be thousands of feet high, casting mile long shadows across the crater floors. In less than an hour you can see a difference in shadow casting. On the floor of large craters, try to locate small impacts craters, that can be numerous in some. No two craters look the same, there is a showcase of features that could keep you busy for years.
Much less detail is observed during the full Moon cycle, when shadowing is at its lowest. Use a filter to "tone down" the brightness of a full Moon. Most scopes come with a lens cap that has a small "hole" that can be removed from the cap allowing only partial light through the primary lens. You may want to cut a ,hole in a peice of cardboard and cover your lens, this will dramaticly cut down the brightness.
For fun, get a good Moon map and start keeping track of the features that you observe. Get a small notebook and detail your findings. With all the amatuer astronomers out there, you would be amazed how few "Moon experts" there really are.