How does an electron microscope work? I am a physics novice.
Google tells me that electron microscopes work much like their optical counterparts -- but the analogy falls apart for me when I think about what I'm "viewing."  Obviously, you can see light through the lenses, but what is the "image" analog for electron microscopes?
Is it at-all like spraying an invisible shape with bullets and examining where collisions took place?  Like if you shot at an invisible car with a tommy gun and were able to make out bullet holes -- so that the more bullets you shoot the better your image?
And, just for completeness, I suspect this implies that the best resolution you can get is the bullet-size, or in this case the size of the electron.  How do you map "objects" or whatever they are considered on that scale if they are smaller than an electron?  Is our perception of how small we can see limited by this cap?
 A: those answers were all pretty heavy for a physics novice!
I think the answer you are looking for is easier than you might think - 
you 'see' light through a microscope's lens because your eyes are great photon detectors. without a detector, a light microscope can't create an image.
an electron microscope (there are various types) simply has other types of detectors. depending on what size scale you are looking on the could variously be detecting reflected electrons (the proper term is backscattered), deflected electrons, emitted light from excited electrons, or even variations in various forces. This is the same for light microscopes, you are simply seeing reflected/emitted light.
there are even electron microscopes that rely on quantum tunneling of electrons, and measure the tunneled current, which changes depending on the distance between microscope tip and object.
the point is, all they do is measure interactions of the wave and the object, in the same way your eyes do with a normal light microscope. a computer (or your brain) then models what was detected to resolve an image.
the only other concept you need is that the resolution of any microscope is proportional to the wavelength used. A smaller wavelength can generate better resolution. So the best you can do with a light microscope is violet light, with a wavelength around 400nm. An electron can be seen as a wave as well, and has a far smaller wavelength, in the range of picometres. Marek's suggestion re:wave-particle duality could help here.
I have been trying to put why small wavelengths mean better resolution into simple terms but it is eluding me. Kinda needs diagrams. Maybe someone else can help?
