An SEM is comprised of a large number of basic systems, all of which need to work in order for the basic machine to function. As any user needs to understand how these things work in order to understand how their actions (or lack of them) can affect their results (or basic functionality of the SEM), then this is the best place to start. I will start with the basics and then address some of the more specific components in a later section.

Control Console:
Most of the parts of the microscope are controlled through the control console, as the name might suggest. Electron beam control (electron lenses, beam deflections, electron gun controls), image processing (linear and nonlinear signal amplification, static framestores, image display(s)), scan generation and synchronization, and vacuum system controls are all principally controlled through the console. This essentially makes up all the bits 'n pieces that constitute the SEM. A traditional SEM console accomplishes this using dedicated electronics for each system, all in one big box. More recent SEM designs have attempted to save money by running most of the controls through a PC or workstation, with control cards outputting control signals to the circuits doing the heavy lifting. (No PC has a 25kV power supply, for example!) One potential advantage of this approach is to automate some operations such as stigmation, focusing and the like through an image analysis feedback loop in the computer. In practice, however, I have yet to see this successfully automated. The disadvantage is usually the inability to operate multiple controls simultaneously, greatly slowing (and impairing) operator control. The cost savings for manufacturers makes this a popular approach, however.

Vacuum System:
The actual 'moving' guts of the 'scope are all either in or on the vacuum system, or a part of it. These include the electron gun and lenses and all the active parts of beam manipulation controls, signal collection devices, and of course, the vacuum pumps, valves, etc.

Electron Guns:
Every electron microscope has an electron gun; this is where the electrons come from to make it an electron microscope...
There are two basic ways of convincing electrons to leave their nice, cozy homes where they are associated with some atom or other. The first method is to dump enough thermal energy in to them so that they are driven off; the second method is to put them in a strong enough electric field so that any of them that stray too far from home will be pulled off. These are rather poetic ways of describing thermionic emission and field emission strategies for an electron source.

A thermionic electron gun consists essentially of a heated wire or compound from which electrons are given enough thermal energy to overcome the work function of the source, combined with an electric potential to give the newly free electrons a direction and velocity. Common materials that are used for these sources are Tungsten (because it has a very high melting temperature, so more thermal energy can be made available); LaB₆; and Ce₆ (because they have both a low work function and a high melting temperature). The heated source is usually held at some potential (anywhere from ~500V to maybe 100kV) negative relative to ground, so that a sample (as well as the rest of the microscope) can be kept at ground.

 A tungsten 'hairpin" type filament.

A field emission gun consists of a sharply pointed tungsten tip held at several kilovolts negative potential relative to a nearby electrode, so that there is a very high potential gradient at the surface of the tungsten tip. The result of this is that the potential energy of an electron as a function of distance from the metal surface has a sharp peak (from the work function), then drops off quickly (due to electron charge traveling through an electric field). Because electrons are quantum particles and have a probability distribution to their location, a certain number of electrons that are nominally at the metal surface will find themselves at some distance from the surface, such that they can reduce their energy by moving further away from the surface! This transport-via-delocalization is called 'tunneling', and is the basis for the field emission effect.

Thermal field emitters enhance the pure field emission effect by giving some thermal energy to the electrons in the metal, so that the required tunneling distance is shorter for successful escape from the surface.

A Schottky emitter is a thermal field emitter that has been further enhanced by doping the surface of the emitter to reduce the work function.

A Schottky field emitter assembly. The outer shiny part is the suppressor electrode; the emitter is a tiny pinprick sticking up through the small hole in the center of the suppressor.

Vacuum Pumps:

There are four types of vacuum pumps that are at least somewhat commonly employed in SEMs. I will go over the basic operational mechanisms and operational parameters of each, then put each into their place in a typical SEM.
Roughing pump/mechanical pump: This is a pretty basic design that takes a large initial volume, squeezes it down into a smaller volume, and expels it at the high-pressure side. These usually involve an oil as a lubricant and gas seal although oil-free models can also be purchased for a considerable premium. Outlet/inlet pressure ratios are typically on the order of 5*105 or so. The high-pressure side can operate at atmospheric pressures, while the low-pressure side is usually limited by the vapor pressure of the pump oil used.
Diffusion pump: This uses a high velocity stream of gas molecules to kinetically 'trap' random gas molecules from the vacuum system that blunder into the stream. These typically consist of three stages, each of which will support pressure ratios of approximately 10:1 or greater. The maximum pressure on the low pressure side is typically around 100mtorr or so, while the maximum pressure on the high pressure side is typically on the order of (maybe) 200 mtorr. More typical operating ranges are around 10-6 torr on the low pressure side, with 5*10-2 torr on the high pressure side.
Turbo pump: A turbo pump is essentially a whole heck of a lot of axial compressors (ala turbine) on really tight tolerances moving at truly frightening speeds. These have the advantages that they have good throughput, pump most gases about equally well, have inlet pressure limits somewhere better than 10-8 torr, have outlet pressure limits pretty close to atmospheric pressure (maybe 10 torr or better, I forget), and can actually be started while being pumped down. The disadvantages include high cost, higher frequency of maintenance required, potential for vibration, and higher sensitivity to foreign object damage. The typical description of a turbo pump failure is of a brief 'scream of anguished metal', followed by the entire vacuum system being filled with aluminum confetti. These typically spin at 60,000-90,000 RPM or so, so a foreign particle, bearings starting to go, etc. will all cause a rather spectacular failure.
Ion pump: This is an entrapment pump, so there is only an inlet, but no outlet pressure. An ion pump works by ionizing any and all stray molecules or atoms that fall into it, then reacting these with (or burying them in) a chunk of metal. Typically these can be thought of as two parallel plates of titanium held at something like 5kV potential relative to each other. When an unsuspecting neutral atom/molecule bumps the + electrode, it suddenly becomes one or more + ions itself, which are then accelerated through the potential between the plates, smacking into the - electrode. As titanium is a very reactive metal, most species will simply form a compound with a nice low vapor pressure, effectively removing them from the pumped volume. The non-reactive species (say Ar) will tend to simply get buried in the Ti, struggling in vain until doomsday to escape their confinement. (Ah, the cruelties of an ion pump!) Most ion pumps are more involved than the simplified form presented here, but this covers the basic idea. Typical refinements include magnets to promote sputtering (new Ti surface) or evaporation of Ti (again, more new Ti surface). A typical ion pump will actually start to function around 10-5 torr or so, but this is really abusive. More typical (better operation) upper pressure limits are more on the order of 10-6 to 10-7 torr. For a pretty new, nicely cared-for ion pump in a really tight system, numbers like 10-12 torr can be achieved. Usually for SEM work (open vacuum system, rubber seals, people abusing the poor things), 10-7 to 10-9 torr are more common.