We’ll do this using a process called Convolution. The idea of convolution is inspired partly by computer science and partly by biology (i.e. mad scientists literally poking cat brains with weird probes to figure out how cats process images).
This idea has been around since the late 1960s. But until recently, training this large of a neural network was just too slow to be useful. But once we figured out how to use 3d graphics cards (which were designed to do matrix multiplication really fast) instead of normal computer processors, working with large neural networks suddenly became practical. In fact, the exact same NVIDIA GeForce GTX 1080 video card that you use to play Overwatch can be used to train neural networks incredibly quickly.