Neptune compared to Earth
Like most gas giants, Neptune's atmosphere is mostly composed of hydrogen and helium, about 80% and 19% respectively. Unlike Saturn and Jupiter, however, Neptune is very icy, earning it, and its relative, Uranus, the title "Ice giant". Neptune contains proportionally large quantities of "ices" like water, ammonia and methane. The outer cloud layer can be as cold as -218 degrees Celsius (that's only 55 Kelvin). It is so cold that methane precipitates in the atmosphere, contributing to the blue color of the planet by absorbing light in the red spectrum and reflecting blue light. Methane is not enough to explain Neptune's color, meaning that there must be some other as of yet unknown agent contributing to the smooth blue that we see.
Neptune has the fastest winds in the entire solar system, speeding up to 2,100 km/h, nearly supersonic. Neptunian winds flow mostly in the opposite direction of the planet's rotation. Generally there is a prograde wind rotation at high latitudes and a retrograde rotation at low latitudes, owing mostly to the "skin effect" and not deeper atmospheric conditions.
The interior of Neptune is mostly composed of ices and rock. The "ice" at the core isn't actually a solid, but materials like water or ammonia. Temperatures can reach up to 5,400 Kelvin at the center, much cooler than either Saturn or Jupiter. The water, ammonia, and methane at the core are compressed significantly by the great pressure on the surface of the planet until they become liquid, forming a conductive water-ammonia ocean. The farther towards the core we go, water begins to ionize until we have free floating hydrogen and oxygen. Even further down, the ionized water crystalizes, leaving free floating hydrogen ions to mingle in a lattice of crystalized oxygen. The magnetic field of Neptune is titled 47 degrees and experiences significant warping with rotation. This field is also quite strong, about 27 times that of earth. It is believed that the odd orientation of the field is due to the movement of conductive materials in the core, like the water-ammonia ocean.
Neptune's interior composition
Probably the last feature of Neptune that I have yet to speak on is its system of rings. Like Saturn and Jupiter, Neptune has rings of dust and ice orbiting it. Like Jupiter, these rings are faint and not nearly as spectacular as Saturn's. Unlike both Saturn and Jupiter, however, Neptune's rings are fragmented, broken up into various arcs. Because of their shaky pattern, these rings are likely short lived.
Many of the planets in our solar system are various shades of reds and yellows, but Neptune offers a nice relief from these "hot" colors with its cool blue clouds, earning it the name of the god of the sea.