A Full Moon occurs once every 28/29 days.
When you see it at 'full' for three nights, it is still waxing/waning but very close to full.
Astronomical tables will give the date and time (to the minute) , when it is full.
The Lunar cycle is once very 28/29 days. During this time it makes one orbit of the Earth. At New Moon, you will not see it, because the Sun's light blinds us from casual observation, except when there is a Solar Eclipse.
At seven days you will see, in the evening, the First Quarter (Half a semicircle).
At fourteen days you will see the Full Moon ( a Full lit circle).
At twenty one days you will see, in the morning, the Last Quarter ( The other Half of a Semi circle).
At twenty eight days, it is back to the New Moon.
Because the Lunar Orbit is NOT co-planar with the Earth's orbit about the Sun, but angled slightly. Also the orbital track is an ellipse, not circular. You will see at the same point in the lunar cycle that the Moon is at different heights in the sky.
It is because of this non-co-planality that eclipses of the Sun and Moon are infrequent.
The Moon and the Sun control the tides(at sea). At New and Full Moons we have Spring tides and at the First and Last Quarters are Neap Tides.
In very clear weather, when the Moon is crescent shaped (New) you can often see the unlit part of the Moon. Country people will say ' The New Moon with the Old Moon in her arms).
The word 'Month' comes from 'Moon/Moonth'.
A woman's menstrual cycle of 28 days, is thought to be biologically driven by the Moon's cycle, as are many others things in nature.