Which way does each crescent face?
☽ looks like a backwards C, with its outer curve on the right. That is how the waxing (growing) moon looks from the Northern Hemisphere, which is why Unicode named it "first quarter moon". ☾ is its mirror image, shaped like a C: the waning moon, named "last quarter moon".
An easy way to remember it is DOC: a moon shaped like a D is growing, an O is full, and a C is shrinking. South of the equator it works the other way around. Fonts differ a little, so check how your crescent looks before you post it. Every moon phase emoji is on the moon symbol page.
What the crescent moon means
A crescent is shorthand for night, sleep and dreams. Phones use it for Do Not Disturb and dark mode, and ⏾ is the official sleep symbol from the set of power button icons added in Unicode 9.0.
The star and crescent ☪︎ is widely associated with Islam and appears on the flags of countries such as Turkey and Pakistan, and 🌙 often accompanies Ramadan greetings. The Red Crescent, the sister movement of the Red Cross, also uses a crescent as its emblem.
Older traditions use it too: alchemists drew the crescent for silver (🜛) and the sun ☉ for gold, and modern pagan groups use the triple moon ☽ ◯ ☾ for the waxing, full and waning moon.
How to type a crescent moon
In Microsoft Word, type 263E and press Alt + X for ☾, or 263D for ☽. The emoji 🌙 is on every emoji keyboard: search for "moon" or "crescent", or press Windows + . on a PC and Control + Command + Space on a Mac.
Text crescents take the color of the text around them, so they suit aesthetic symbols and minimalist bios. For a darker look, see the black moon symbol page.