One cycle: about 29½ days
At new moon the moon is between us and the Sun and its lit side faces away, so we see almost nothing. Over the next two weeks it waxes — a crescent, then the first quarter (half lit), then gibbous — until at full moon it is on the far side of the Earth and fully lit. Then it wanes back through the last quarter to the next new moon.
A full cycle takes on average 29.53 days, but individual cycles vary because the moon's orbit is not a perfect circle. Between 2025 and 2030 the shortest is 29 days 7 hours and the longest 29 days 20 hours.
Twelve or thirteen full moons
Twelve cycles take about 354 days, so most years have 12 full moons, and roughly every two or three years there is room for a 13th. In the next ten years that happens in 2026, 2028, 2031 and 2034.
What is a blue moon?
Today a "blue moon" usually means the second full moon in one calendar month. (An older definition is the third of four full moons in a season.) It has nothing to do with colour. Counting in UTC, the next blue moons are in May 2026, December 2028, September 2031 and July 2034 — in some time zones a full moon near midnight can fall in a different month.
Why there isn't an eclipse every month
At every new moon the moon passes between the Earth and the Sun, and at every full moon it is behind the Earth — so why aren't there eclipses every two weeks? Because the moon's orbit is tilted about 5° to the Earth's, it usually passes a little above or below the Sun or the Earth's shadow. Eclipses only happen when a new or full moon falls near one of the two places where the orbits cross, which lines up about every six months.