Please excuse me if my question is not well-worded. My background is pure mathematics and I am not familiar with engineering, but sometimes I feel fascinated by the things engineers have achieved.
Anyway, when I read about neuroscience or nano-engineering, I read things like engineers have been able to arrange atoms on an extremely small metal (like the IBM movie) or neuroscientists can measure voltage changes of an ion-channel inside the membrane which is extremely small.
When I was a child, I learned that levers enable us to move extremely heavy objects but we were never told how engineers work with extremely small objects. For example, how is it possible for neuroscientists to insert an electrode under the membrane of a single neuron to measure voltage changes? Or how is it possible for scientists at IBM to arrange atoms in an IBM shape? Or if I want to build a robotic arm that it can move with a precision under 1mm, how can that be done?
I know how microscopes and scanners work, I don't understand how moving things in very small regions work. In short, what I am looking for is a short list of methods or tools that engineers use to tackle engineering challenges at extremely small scales.