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Here is a useful mnemonic for distinguishing whether a near-full Moon is coming or going:

Another way of telling is this:

L-E-FT hand curve = D-E-CREASING.
R-I-GHT hand curve = -I-NCREASING.

Using the natural curve of the hand from first finger to thumb, if the Moon's crescent fits the curve of the L-E-FT hand, then it is D-E-CREASING, but if the crescent fits the R-I-GHT hand, then it is -I-NCREASING.

There are several "types" of moon, each with their own description:

Blue Moon: the second of two Full Moons occurring in the same month. The lunar cycle is 27.3217 Earth days in length (or 27 days 7hrs. and 43m.), and thus it is rare for two Full Moons to occur in the same month - in fact only once every 21/2 years - hence the term "once in a Blue Moon.."

Crescent Moon: occurring in the two periods just before and after new moon, when the bright part is less than a semi-circle and gives the Moon the appearance of "horns".

Gibbous Moon: the opposite of a crescent Moon, these are the two periods near Full Moon when the bright part is greater than a semi-circle but less than a circle; from the term meaning convex or protuberant.

Full Moon: When totally visible, the opposite of a New Moon. The Moon shines by reflected light from the Sun, and when the Earth passes between it and the Sun (once every 27¹/₃ days, usually on a slightly different crossing-plane) it becomes a complete circle and is then called "full".

Half Moon: the period exactly halfway between a New Moon and a Full Moon, when the Moon appears to be an exact semi-circle of light. There are two Half Moons in a lunar cycle.

Harvest Moon: the Full Moon nearest the autumnal equinox, rising for several days at about the same time as sunset and providing enough extension of light to enable farmers to continue harvesting after sundown.

Hunters Moon: the next full moon after Harvest Moon, so called because it coincides with the start of the hunting season and gives extra light beneficial to hunters out stalking game in the evenings...

New Moon: when virtually invisible, the opposite of a Full Moon. The Moon shines by reflected light from the Sun, and when it passes between the Earth and the Sun (once every 27¹/₃ days, usually on a slightly different crossing-plane) it becomes invisible as the reflecting surface points entirely away from the Earth. It is then called "new" because it is about to start a new lunar cycle.

Paschal Moon: the first Full Moon after spring equinox (around March 21st). Easter Sunday can vary from 22nd March to 25th April, being the first Sunday after the Paschal Full Moon. The word Paschal comes from the Hebrew "pesach" meaning Passover, and Paschaltide is the Anglican Church period from Palm Sunday to Pentecost.

Earth's moon is the 15th largest in size of the planetary bodies in the solar system.