The surface of a neutron star is not made of neutron degenerate matter, only its interior. A neutron star is layered, like an onion, with the atmosphere, the surface and the interior. There are still atoms of chemical elements on the surface, and we can measure the spectra of them (and they are really weird, due to extreme magnetic fields). So, while it's true that you would get flattened if you attempted to stand on the surface of a neutron star, you wouldn't be turned into neutrons. But before you'd get flattened, you'd first be stretched like a spaghetti, due to immense tidal forces (the difference between the gravity acting on your feet and on your head). And you'd be vaporized, since neutron stars are very, very hot. Oh, and the intensity of the magnetic field would completely re-arrange your atoms, destroying all chemical bonds. And the radiation... And to an outside observer, your death would happen in very slow motion, due to relativistic effects (well, not really, you'd be dead much sooner while approaching the star, but it's a grizzly thought to entertain :D ).
The surface of a neutron star is made of a mixture of normal, atomic matter (though, their structure is all warped due to extreme magnetic fields) and free nuclei and electrons (plasma), below the surface we find a layer of electron degenerate matter, just like inside a white dwarf. As we go deeper and deeper, we find atomic nuclei with more and more neutrons, and at a certain point, there is just a sea of neutrons, resisting gravity only due to Pauli's exclusion principle. In the centres of more massive neutrons stars, there might possibly be exist a weird type of matter called quark-gluon plasma.
Also, it is true that neutron stars are smooth, but they are not perfectly smooth. The surface of a neutron star can be quite active, there might be something similar to plate tectonics there. What we know for certain is that there are starquakes happening on neutron stars which we can detect by tiny changes of pulsar frequencies.Show less