There are fourteen known moons of Neptune. They are cold, dark and very hard to see. In fact only one was seen directly from Earth via telescope.
Triton, the largest satellite was discovered by William Lassell in 1846. Lassell made his find just 17 days after Neptune itself was discovered.
The next to be discovered is actually the third in size and it's the moon Nereid.
Nereid was found by Gerald Kuiper by studying pictures of Neptune in 1949.
The next six, including the second largest Proteus, were discovered by the Voyager 2 satellite in 1989.
In 2002 the next four was found using telescope images. These moons are so faint and far away from Neptune that Voyager missed them. They are about 25th magnitude. The main telescopes used to find these moons are 4.0 and 3.6 meters across. That's about 13ft and just under 12ft respectively.
Psamathe was discovered in 2003 by a team using the 27ft (8.2meter) Subaru telescope in Japan.
A 14th moon has been
discovered in 2013.
Triton is the largest of the moons of Neptune, and the only one you might see from the backyard.
With an apparent magnitude of 13.5,
Triton could be visible from very dark skies and perfect seeing
conditions in a 10in(250mm) telescope like this one.
Of course you should be happy to just locate Neptune itself.
Triton is the only large, major satellite in the Solar System with a retrograde orbit. This means that it orbits Neptune in the opposite direction as Neptune orbits the Sun. Many irregular moons of the other large planets do this as well but they are fairly small and oddly shaped.
Neptune is the Roman god of the sea and the Greek equivalent to Poseidon. As such Neptune's moons are named after various water gods and deities.
Triton, Proteus, Despina and Thalassa are the children of Poseidon.
The Nereids were sea nymphs who often accompanied Poseidon and were helpful to sailors during storms.
The Naiads were fresh water nymphs.
In order of orbit from closet to the planet to farthest away here are the moons of Neptune:
Naiad, Thalassa, Despina, and Galatea were all discovered by Voyager 2 during its trip to Neptune in 1989.
Larissa was found by a team during an occultation in 1981. Confirmed and recovered by Voyager in 1989.
S/2004 N1 was found in 2013 by an
astronomer looking at Hubble Telescope images from 2004-2009 of
Neptune's rings. An official name has not been made yet.
Proteus(pictured at left) the 2nd largest of Neptune's moons was discovered by Voyager in 1989.
Triton is next in orbital distance.
Nereid comes next and is the 3rd largest moon taking almost an Earth year to orbit Neptune once.
Halimede is next and takes just over 5 years to orbit.
Sao takes just under 8 years to orbit and Laomedeia orbits in 8.5 years. These are 3 of the 4 discovered in 2002 along with the most distant moon Neso.
Between Laomedeia and Neso is Psamathe.
Psamathe orbits in just under 25 years and Neso in 26.5 years.