Astronomers are not too certain about this, but the best theory we have suggests that the pulses are generated like this:
Pulsars are spinning very rapidly, up to 30 times a second ( 1800 RPM!) and are known to have powerful magnetic fields of several TRILLION Gauss. At the surface of a pulsar, this produces very large currents of charged particles, mostly electrons which have been ripped from the surface of the neutron star. Now, because the magnetic field of a pulsar looks like a bar magnet, the field lines at some parts of the neutron star are parallel to its surface and prevent the charged particles from getting too far away from the surface of the pulsar, however, near the magnetic poles, the field lines are perpendicular to the surface and some of them extend thousands of kilometers into space. The charged particle currents may be accelerated along these open field lines, spiraling in very tight helical orbits and emit electromagnetic radiation. As the neutron star spins, these beams sweep past the Earth and we see the pulses much like a lighthouse beacon. There is much we do not understand about this process. The pulses have a complex structure in time, often with sub-pulses that grow and fade in strength. There is the suggestion that there may be more than one beam generated subdivided into yet smaller beams, each producing its own component to the over all pulse pattern.
The actual process of particle acceleration and radiation production is not fully known. Also, somehow, the pulsar is able to energize an entire nebula of charged particles extending over one light year across, despite the fact that the pulsar is only about 20 kilometers in diameter! Pulsars also experience 'glitches' in which they momentarily speed up their rotation. Some think this is due to 'earthquakes' in the centimeter- thick crust which cause the neutron star to reduce its radius slightly, causing it to spin-up due to conservation of angular momentum. The reason that these starquakes occur is not fully understood either.