Moon Phases Almanac
Each of the eight named phases is a specific day-count into the 29.53-day cycle with a specific lit fraction and a specific window above the horizon — learn the eight rows and you can name anything you see.
The cycle runs new, waxing crescent, first quarter, waxing gibbous, full, waning gibbous, last quarter, waning crescent, and back to new. The four principal marks — new, first quarter, full, last quarter — fall 7.38 days apart, at days 0, 7.38, 14.77 and 22.15; the four intermediate names sit near the midpoints, around days 3.7, 11.1, 18.5 and 25.8.
Lit fractions in a normal waxing run are 0%, about 25%, 50%, about 75% and 100%, and the waning half repeats the same five steps mirrored. Because illumination follows (1 − cos elongation) / 2, the percentage changes fastest around the quarters and slowest near new and full — a crescent becomes a quarter within days, while a nearly full disk lingers.
On narrow screens, swipe or scroll the plate sideways.
Each phase also owns a window of the day. New moon keeps the Sun's hours and is effectively unobservable; first quarter is visible from about noon to midnight; full is up all night; last quarter belongs to the hours after midnight and shows the limb with the large craters such as Tycho. The intermediate phases inherit in-between windows: waxing crescent appears low in evening twilight, waxing gibbous dominates the evening, waning gibbous the late evening, and waning crescent the pre-dawn sky.
To name what you are looking at, combine two readings: lit fraction first, then the clock. A 75% disk in the evening is waxing gibbous; the same 75% disk before sunrise is waning gibbous. A 50% disk high at sunset is first quarter; a 50% disk high at dawn is last quarter.
The rise and set logic behind those windows is worked through on Moonrise and Moonset (/moonrise-and-moonset), and the day-count arithmetic for any calendar date is on How to Calculate the Moon Phase for Any Date (/calculate-moon-phase).
Further reading