Neutron stars were predicted before they were ever detected. It's a bizarre concept - up to 3 solar masses (3 Suns!) crammed into a sphere about 20 km in diameter. You would not ask Scotty to beam you down to the surface of one; the gravity would quickly reduce you to a one-atom thick smear.
Neutron stars are figured to result from Type II supernova explosions. As the iron core collapses, some of the overlying material falls in with it. The collapse occurs at a significant fraction (30%) of the speed of light. All the infalling material is crushed in an incredible inferno of photons and particles until protons and electrons are combined into neutrons. When the neutrons become packed together, another quantum force called neutron degeneracy takes over and stops the collapse. The thing becomes a solid ball of neutrons. It's not made of any recognizable element; there aren't any protons. It's just solid matter, at least as solid as possible. It's density is on the order of 1015 times that of the Sun. Remember - it can be up to 3 solar masses crammed into a ball about 20 km in diameter.
The gravity is so high because you can get so close to the center of it. Consider the Sun: if you had a magic spacecraft that would let you get real close to the photosphere, you would still be 430,000 miles from the center of the Sun. Gravitational acceleration is GM/r2 and r is large. You can get down to 10 km (6 miles) from the center of a neutron star, so the gravitational acceleration gets VERY large. Weird things happen only VERY close to such an object.
One of those things is the process of spaghettification. You get drawn out into a long noodle as you approach the object.
Another thing to remember is that mass is mass, whatever it may be. The Sun would have exactly the same gravitational properties if it were a 1 solar mass white dwarf or neutron star, a normal star, or 1 solar mass of stale pizza. From 1 AU out they all gravitate the same.
Given their small size, neutron stars should be VERY hard to see. At 20 km diameter, they should be VERY dim objects. It turns out that some of them rotate very rapidly and appear to pulse in radio and visible wavelengths. Slow pulsars have periods of several seconds while fast one pulse as fast as 1000 times per second!
The width of the actual pulse (not the spacing) carries some information about the maximum size of the object that emitted the pulse. We used the Sun for a thought experiment. First - we need to recall (from above) that the Sun's radius is 430,000 miles, or about 690,000 km. At light speed, that's about 2.3 seconds; not large but not zero either!
Mow suppose that the Sun could suddenly change brightness all over at the same time (as seen from the center). What would it look like from here? Well, the change first reaches us from the center of the Sun as we see it. That is the closest point, so that gets here first. The change will reach us from the edge of the Sun's disk 2.3 seconds later. We will see the change spread out from the center of the disk toward the edge, taking 2.3 seconds to do so. Note carefully: from the center of the Sun (equidistant from all points on the photosphere), the change would be seen all over the Sun at the same instant.
How about from here? All points on the photosphere are NOT equidistant from us. The center of the Sun's disk in the sky is 2.3 light-seconds closer to us than the edge. This geometry causes a uniform change to be smeared out over 2.3 seconds!
Now let's assume that the change (whatever it is) lasts only 0.3 seconds. Very short. Now what happens. We see the change appear in the center of the disk - like before. It starts to spread outward, as before. Now, though, the change undoes itself in 0.3 seconds, before the leading edge has gotten very far. We see a 0.3 second wide circle of change spreading outward, taking 2.3 seconds to reach the edge. The change is seen only on a thin circle, never the entire disk of the Sun. A pulse that short is so smeared by the Sun's radius that is not significant.
The significance of this is that the width of the pulse tells us something about the emitting object: it can't be any larger (radius) than the pulse length. The radius is, of course, measured in light-seconds.
Now consider a pulsar pulsing 30 times per second. That's 0.033333 seconds between pulses. The pulses themselves are much narrower than the spacing. Suppose that the pulses are about 0.003 seconds wide. At light speed that's about 900 km, or about 560 miles. The emitting source can't be any larger than that! That is MUCH smaller than any white dwarf!
The only object that could be imagined to rotate fast enough to be a pulsar and not fly apart from the rapid rotation was a neutron star. They CAN spin that fast and not fly apart; a white dwarf cannot.