Gustav Fechner. Whereas Descartes thought that the brain communicated with the body through a series of tubes (that's right, Ted Stevens), Fechner demonstrated that it was electricity. Not only that, but he showed that it took time for the brain (of a frog) to communicate with its leg. It was previously thought that brain-body communication was immediate. But now, it was a very very very short amount of time. But that instant could now be measured. And Fechner, and his fellow German physiologists went about measuring the relationship between the physics in the world (like light, or sound, or electric shock) and our psychological experience of the physics. Now that each could be measured, we had a psychophysics. Fechner was born in 1801, and so most of this work was in the early and middle 1800's.
Many persons nowadays seem to think that any conclusion must be very scientific if the arguments in favor of it are derived from twitching of frogs' legs—especially if the frogs are decapitated—and that—on the other hand—any doctrine chiefly vouched for by the feelings of human beings—with heads on their shoulders—must be benighted and superstitious.But there were now neurons, and soon there would be neurons working together. Donald Hebb, and much later, Eric Kandel, began to discover the way, at the cellular level, that neurons communicate and remember. As the decades went by, different animals (from sea slugs, to cats, to, in very rare cases, monkeys) had different parts of their brains surgically changed, and their behavior was recorded. A map of the brain was beginning to emerge.
I'll mention a few more cases of changing the brain, then observing behavior. The first was an experimental surgery to relieve extreme epilepsy. It was 1953, and 27-year-old Henry Moliason was referred to a reckless doctor named William Beecher Scoville. Henry's epilepsy was localized to a structure in his brain located in the middle of his temporal lobes, on the side, tucked underneath. Scoville removed an entire section of his brain around this area, and thereby improved Henry's epilepsy. After recovery, Henry could see, hear, walk, talk, breathe, eat and drink just fine. But he needed to be institutionalized for the rest of his life. Why? Because Scoville unwittingly removed Henry's ability to make new memories. Someone could go into Henry's room, meet him, leave, wait a minute, then reenter and meet Henry again. For Henry, it would be "for the first time". Later studies showed that Henry could learn new skills, but would never remember having practiced them, so the memory damaged seemed to be only his conscious, or explicit memory.
In the past decade a new technology has allowed us to selectively "damage" human brains, but only temporarily. Imagine applying a little shot of anesthesia and paralysis to a certain small group of neurons and seeing what happens. This is exactly (ok, not exactly, but close enough) what transcranial magnetic stimulation is able to do. Zap Broca's area with a targeted magnetic field, whammo, you can't talk. For a few minutes. Then you are fine.
While Henry Moliason (or Patient HM, as he was known for most of his life in the memory literature) was a uniquely tragic, yet informative patient, for over a hundred years, cognitive neuroscientists have been changing the brains of animals and observing and recording the ensuring behavior. This has given us tremendous insight into how the mind and brain are linked, from organization of the visual system, to different memory systems, to systems of how our brains control our muscles. With the progression of technology to TMS, we are now able to very selectively "damage" human brains, and observe the associated behavior. But this is built on an increasingly detailed map of the brain, which in turn was surveyed using thousands of human and animal studies.