When you look at individual atoms, what are you actually seeing?

That kind of image was probably from a scanning-tunnelling electron microscope on which you get a very sharp point where it's so sharp it's probably only got one or two atoms on the end. They scan that very slowly across the surface of a material. With a scanning-tunnelling electron microscope you measure the amount of electric current going between that and the material. You apply a tiny voltage, measure the current between that tip and the surface. You're actually measuring the resistance of the surface. There are other similar images where you can measure the force on that tip. You're basically measuring the force between the end of the tip and the surface at the bottom. If the atoms are higher up the force will go up and vice versa.