Phase Finder
The Moon's phase is where it is in its orbit, not a shape the Moon has.
The Sun lights one half of the Moon, and it lights the same half all month long. The Moon never changes shape. What changes is where the Moon is standing in its circle around Earth, and so how much of that lit half is pointing our way.
That is the whole trick. The eight phases are eight places on one circle, not eight different Moons. A new moon is the Moon out in front of us, nearly in line with the Sun, with its dark side turned towards us. A full moon is the Moon behind us, with Earth in the middle, showing us the whole lit half. The crescents and the gibbous shapes are the places in between.
The Moon takes about a month to go all the way round, so one week is about a quarter of the way. That is why the phase you see tonight tells you what you will see next week.
One name to watch for: the phase a quarter of the way back from a new moon is called the last quarter, and some books call the very same phase the third quarter.