Neutron Stars and Pulsars
Neutron stars are a hyper-dense form of dead star composed almost entirely of neutrons. A sub-class of neutron stars are called pulsars - so-named because, relative to Earth, they emit regular pulses of EM radiation. This page talks about both neutron stars and pulsars.
Neutron Star Formation
A neutron star is a star made entirely out of neutrons, as the name suggests. These are the remains of stars that had between 1.4 and 9 times the mass of our sun (solar masses). After a star goes nova, the remaining core collapses while the outer layers are blasted off into space to create a nebula. Gravity shrinks and condenses the core into a sphere about the size of Manhattan (25 km (15 mile) diameter) within a few seconds. A neutron star is so dense that a pinhead's worth of material from one would weigh as much as a supertanker.
Under ordinary classical mechanics, this would not be possible. Atoms are mostly empty space as a result of one of the four fundamental forces: the Electro-Magnetic (EM) Force. This keeps the electrons out of the atom's nucleus. However, the most important principle that comes into play is the Pauli Exclusion Principle and electron degeneracy. This says that no two electrons can occupy the same quantum state. This boils down to no two electrons being able to occupy the same place.
What happens in neutron stars is that the Pauli Exclusion Principle is broken. As more mass is piled on (up to 1.44 solar masses, also called the Chandraskhar Limit), the densities get higher and the electrons are boosted to higher energy levels. Eventually, the required speed for the electrons is greater than that of light in order to support the electron degeneracy.
Once this happens, the star collapses, for the electron degeneracy can no longer support it. In a few brief seconds, the star collapses down to a neutron star, supported by neutron degeneracy, where no two neutrons can occupy the same quantum state. This keeps the neutron star from collapsing further, until its critical mass is reached at about 3 solar masses. Then, the collapse is to a black hole.
Neutron Star Anatomy
A neutron star's anatomy is very simple, and it has three main layers: A solid core, a "liquid" mantle, and a thin, solid crust. Neutron stars also have a very tiny (a few centimeters - about an inch) atmosphere, but this is not very important in the functioning of the star. Typical sizes for these parts are about 1 km for the crust, and 10 km for the mantle and core combined.
A neutron star also has two axes - a magnetic one and an axis of rotation. Just as Earth's magnetic axis does not run through the geographic poles, a neutron star's axes rarely line up. (Please bare in mind that the schematic at the right is not drawn to scale.)
A pulsar is the same object as a neutron star, but with one added feature. A pulsar emits two very high-energy beams into space, concentrated along its magnetic axis (the magnetic field is around one trillion (1,000,000,000,000) times that of the Earth's). The beams are made of material usually stolen from a companion star, and the particles are accelerated to speeds as great as 20% that of light.
Pulsars (and neutron stars) spin very rapidly (as seen from Earth), most at about once every second (the record for the fastest is at 642 rotations per second, and the record for the slowest is one spin every 4.308 seconds). The reason for the rapidity in the spin is due to the law of conservation of angular momentum. This law has such implications that if an object is spinning at a certain speed, then is shrunk but keeps the same mass, it must increase its rotation rate.
For an example of this, take a ball attached to a string and spin it around in such a way that the string wraps around your hand or wrist. You will notice that as the ball comes in closer, it rotates more quickly. Also, once it is wrapped, go the other way so that it unwraps. You will notice that the ball goes more slowly as the string is let out. Another practical example is to watch a figure skater - if they want to spin quickly, they will draw their arms and leg in closer to their body, and in order to slow down, they spread out.
Pulsars will eventually slow down and stop spinning, due to energy lost as it sends off ripples in space (also called gravitational waves, that emanate from all moving massive objects; the waves travel at the speed of light). It will then be seen as an ordinary neutron star because if the beams no longer sweep past Earth we can't see it "pulsing".