How does the moon make it's crescent shape?

The only time the Moon is EXACTLY in the new phase is when we're having a solar eclipse. At most of the new moons, the Moon is just a bit above or a bit below the Sun in the sky. And the Moon is only EXACTLY new for an hour or so; the Moon moves fairly quickly across the Earth. So when you're seeing the sliver of Moon at sunrise or sunset, you're actually seeing a Moon that is a few hours before or a few hours after it is precisely "new".