It really depends on what you mean by the surface of Neptune.
Unlike the four inner planets (including Earth), Neptune doesn't have a sold surface one could walk around on, though it is possible in theory for a probe to 'float' upon its liquid mantle.
This mantle is actually the third of four 'levels' comprising the inner structure of Neptune.
Below, in the bulk of Neptune's atmosphere, we find hydrogen, helium, methane (which gives the planet its blue color), with comparatively minute amounts of hydrogen deuteride and ethane, interspersed with clouds of water, ammonia, hydrogen sulfide and aluminium sulfide.
What is the mantle of Neptune like?
Once we reach the mantle of Neptune, we find a vast, slushy, hot ocean of water, ammonia and methane. Scientists have suggested that pressures are so great at the bottom of the mantle region, there may exist 'icebergs' of liquid diamond!
The core of Neptune, the mass of which is slightly larger than the entire Earth, is made of iron, nickel and silicates, which are mineral compounds also found on Earth, such as hexafluorosilicate.
Learn more about the atmosphere of this fascinating planet by watching this short presentation given by an astrophysicist on YouTube: