Computers do such incredibly complex things these days, it can be hard to remember that it's all done by a series of incredibly small switches called transistors, and all of the data processing that a computer does is a matter of deciding whether some switches should be on or off depending on the state of other switches (including the switches that make up working memory).
Computer chips these days are so complex involving typically billions of switches just in the central processor, and so they can't be designed by hand. But decades ago the first widely used processors were designed manually and were works of art.
It's possible to see what these looked like and how they worked using various on-line simulations. My favourite is http://www.visual6502.org/JSSim/ which shows the operation of a simple 8-bit processor with only thousands of switches.