The Waxing Crescent
A thin lit sliver, growing. In the northern hemisphere the lit edge is on the right; south of the equator it is on the left.
Where to look: Rises mid-morning and sets a few hours after the Sun — the low evening crescent in the west, and the reason 'new moon' and 'first sighting' mean different things to different calendars.
This is the phase that starts months. A lunar calendar begins when somebody sees this crescent, which is why the start of Ramadan can differ by a day between countries that are looking at the same sky through different amounts of cloud. It is also the best phase for earthshine: the unlit part of the disc glows faintly, lit by sunlight bounced off Earth.
Commonly muddled: The horns point away from the Sun, always. If a drawing has them pointing the wrong way, the drawing is wrong.