As the Moon orbits Earth, its phases create various illuminations of different parts of its surface. For optimal viewing of craters and mountain ranges in sharp relief, wait until its first quarter phase (which occurs between noon and midnight and shows half of the Moon visible) occurs - at which time half of it can be seen clearly.
A "half moon" may be deceptively misleading; lunar phases that only illuminate half the Moon actually show more like one-third than half due to their closeness between Earth and Sun; therefore more surface area of their surface becomes visible than expected.
Keep an eye out for the lunar halo, created when thin high-altitude cirrus clouds scatter light from the Moon through thin gaps between their fibers, producing an 18-22deg circle of white light surrounding deep gibbous or full Moons. In folklore, this phenomenon was believed to be an indicator that rain was imminent.
Binoculars or telescope users might want to observe the Moon two or three days past first quarter for maximum effectiveness. When viewing through a telescope, shadows on its surface become easily discernible, revealing details not visible during other lunar phases; you might even spot bright streaks corresponding to Copernicus and Tycho craters!
