Germ Theory Beginnings
Scientists like Louis Pasteur and Robert Koch laid the groundwork for understanding that germs were a thing.
Louis did it by discovering that fermentation was caused by living organisms. Later he went on to discover multiple strains of bacteria. This was groundbreaking because Louis proved that living things could be so terribly small, among other implications of his research.
Robert Koch and his lab proved the link between micro-organisms and sickness by using anthrax. Koch's work snaked its way through medical community discourse and was eventually presented to the public as a parallel to poison (more on that later).
Medical Community Turbulence
Early claims of microbial cultures infecting humans kicked off a torrent of disagreements about what the microorganisms were, how they behaved, how small they were, how good the methodology was that proved their existence, and the like. Phyllis Allen Richmond wrote a famous paper called "American attitudes toward the germ theory of disease, 1860-1880," where she talks about the low acceptance rate of germ theory among American doctors.
There were a few reasons Americans were slow to adopt germ theory:
Researchers' understanding of germs was extremely limited, and not everyone agreed micro-organisms were harmful to peoples' health.
Even if germs were responsible for disease, nobody had figured out how to combat the microbes.
The American research landscape was in its early adolescence, and so medical researchers didn't have much money and manpower to waste on what they assumed were crazy European notions.
American medical schools were more of a commercial enterprise than European schools, so the quality of doctors graduating were much lower than their European counterparts. And fewer committed themselves to rigorous research post-graduation. It was a more capitalist landscape.
Now, it's important to note that European doctors also dissented against germ theory. Their infighting helped prevent American interest in the notion of germ theory for awhile. Also there was that little matter that destabilized America in the 1860s, requiring time for us to rebuild our infrastructure.
Medical Acceptance
For America, 1875 was when our medical community did a hard 180 and our attitude went from aloof skepticism to a stark appreciation for the latest research. This was the period that most outgoing students from medical schools believed in germ theory, which coincided with widespread acceptance among those at the top of the field. Medical literature began wildly publishing on germ theory in the mid-1870s and it quickly became THE thing to study. Franklin Clum from Yale in 1875 was the first to associate germs with poison.
The two biggest European medical researchers of the day were the Germans, who adopted a cavalier, experimental approach to studying germs, and the French were stoic empiricists who all but swore fealty to their strict adoption of the scientific method. For obvious reasons these polar approaches had their limitations, which allowed Americans who were free of those particular constraints (and all the weaknesses attached) to drastically redefine the field without institutional checks on their progress.
By the mid 1880s, the term "germ" had become a confusing catch-all for everyone. For a long time, parasites and viruses and bacteria were all confused with one another. Once those got sorted out, then it took awhile for researchers to discover that different ailments are caused by different microbes, which kicked off more infighting. Laboratory evidence was often dismissed for book knowledge of the day, and even the people who were pro-germ theory advocates noted their methodology was flawed. This included, very notably, Edward P. Hurd who in an 1874 article he wrote for the Boston Medical and Surgical Journal was somewhat apologetic for his own research and the tenuous methods and assumptions it relied on.
Note: at this point, in the 1880s, American and European medical researchers were now working together on equal footing. Everyone was equally flabbergasted about germs.
Post-Medical Community Acceptance
Once the doctors all got their crap together, it didn't take long to figure out which things were really bad for sickness, like poop. Nor did it take long for doctors to find out various aspects of hygiene, like the benefits of handwashing. From there, it was a matter of conveying these complicated new ideas to the public.
This was mostly done through newspaper articles, word-of-mouth, and doctor-patient interactions. In other words, it was a sustained campaign intended to saturate the public with knowledge. And the germ theory advocates relied heavily on metaphors:
- Combustion. Sawdust was an extremely popular metaphor for showing how germs will continue to consume something as long as it has fuel. Everyone knew sawdust was explosive, and doctors would point out that germs envelop and consume a thing until it's gone, just like fire. This scared the shit out of people, but it certainly got the point across. Germ theory advocate Karl Liebermeister wrote in 1874 "A burning shaving can set fire to a house and an entire city. The chemical process of burning multiplies itself ad infinitum, so long as combustible material and oxygen are present under favoring circumstances."
- Poison. Poison was really effective at conveying disease. If you ingest poison, you die. So it's not difficult to make the case that if you ingested millions of tiny poisonous animals, you would also die. It's weird to think about, but the connection between "sickness" and "germs" took awhile to combine—for doctors and the general public.
- Agricultural Allusions. America was still largely agricultural and rural at that point, so agricultural parallels were common. For instance, in order to show that different germs exist, which means each germ type is responsible for contributing to one disease and one disease only, William Mays in 1880 wrote germ likeness is akin to "an oak coming from an oak, a grape from a grape."
- Evolution. In the 19th century the theory of evolution had none of the political baggage that's attached to it today, and near everyone accepted it as fact. In the 1880s, doctors began to note some microbes' phenomenal ability to change in a relatively short amount of time. This strengthened the public's trust once they felt evolution validated germ theory. Not a literary device, I know! But it was an important factor in cultural acceptance.
The Information Campaign & Floor-Length Dresses
The campaign for hand-washing began in earnest in the 1890s. The importance of showering became known. This was all pretty routine, and the general public had an easier time adopting germ theory and germ prevention methods than their medical counterparts (to be fair, they had far less knowledge to drive any possible arguments).
There were other interesting developments that took longer to root out. For instance, one of the big reasons that women's fashion went from floor-length dresses to ankle-length at the turn of the 20th century was that it was discovered that Scarlet Fever cases were way more frequent and severe with women who wore floor-length clothing. The germs were picked up by the garments trailing on the floor, and then their population would explode in the confines of the sweaty clothing. (Another reason dress hem rose was practical—bicycles were in and women couldn't ride bikes in long clothes. I'm sure there are more reasons. But I digress.)
Doctors and women's tailors were the ones responsible for conveying this information to women. Also by that time the government was printing a lot more information to distribute to the general public. So it is likely that educated women—especially those living in urban areas—might've received something in the mail, found a handout at a store, etc.
By the 20th century, hygiene was universally accepted and seen by major sections of the country as a civic duty to perform, lest you get your neighbors sick. So any new discovery, like the connection between Scarlet Fever and floor-length dresses, would've become common knowledge quickly. And there was peer pressure associated with these discoveries.
One final note: humans were spread out for most of human history & the 1800s saw a massive swelling of people into big cities. The lower classes had predictably short lifespans and urban areas of that time were massive population sinks. Serious illnesses went from isolated outbreaks in the country to huge, social problems in the city. This made it easier for the general public to adopt germ theory, who were desperate for good explanations for the concentrated outbreaks that had become known as a curiously urban issue.
I probably made the individual discoveries seem more chronological than they really were—there was a lot of overlap in the confusing race to investigate microbes. But hopefully that answers your questions somewhat.
Sources:
Tomes, Nancy. The Gospel of Germs. Sept 1999. Print. pp. 368.
Richmond, Phyllis Allen. "American Attitudes Toward the Germ Theory of Disease (1860-1880). Journal of the History of Medicine and Allied Sciences. Vol. 9, No. 4 (Oct 1954), pp. 428-454. https://www.jstor.org/stable/24619485?seq=1#page_scan_tab_contents
Tomes, Nancy. "American Attitudes toward the Germ Theory of Disease: Phyllis Allen Richmond Revisited" Oxford University Press. 1997. https://academic.oup.com/jhmas/article/52/1/17/741186
I can offer a partial answer to this question in terms of when medical authorities first realised that handwashing was important. Ignaz Semmelweis was one of three oft-cited figures in medical history, all discovering similar things about infectious diseases at more or less the same time (the middle of the 19th century), the others being Florence Nightingale who demonstrated the importance of proper sanitation in field hospitals and Jon Snow who traced a cholera outbreak to a water pump.
Semmelweis noticed that the maternal mortality rate following childbirth was almost ten times higher if the birth was attended by a doctor rather than a midwife. One of his hypotheses was that it might be because the doctors were performing autopsies before attending the maternity ward.
Dr Semmelweis initiated a mandatory hand washing policy for medical students and physicians. In a controlled trial using a chloride of lime solution the mortality rate fell to about 2%—down to the same level as the midwives. Later he started washing the medical instruments and the rate decreased to about 1%.
Pretty impressive. But his findings did not go down well with the established authorities of the day and it took another few decades for these ideas to become widely accepted:
His superior, Professor Klein, a member of the academic “old guard”, did not accept his conclusions. Klein thought the lower mortality was due to the hospital’s new ventilation system, an idea that fitted the then popular miasmatic theory of disease. Semmelweis convinced a number of young faculty members who supported him. They were to become leaders of the next academic generation who would make the Allgemeine Krankenhaus the world’s greatest teaching hospital for the next half century.
...
Although Dr Semmelweis was the first healthcare professional to demonstrate experimentally that hand washing could prevent infections it was not until approximately two decades after his death that his work was revisited and he was given credit. Only after Pasteur, Koch, and Lister had produced more evidence of the germ theory and antiseptic techniques was the value of hand washing appreciated.
Nightingale had a similar experience with the British medical establishment. You can spot the author's sense of burning injustice from the site url in the link above, florence-nightingale-avenging-angel:
Well, this is not what Nightingale accused him of saying (“practically unavoidable”). One could hardly say that Simon was wrong to maintain that not all deaths from epidemics could be avoided. But I dug out Simon’s rare original 1858 paper and found that he had written then “A further, practically speaking, unavoidable, cause of premature death in every civilised country is the risk of its current contagions.” So he had said, as Nightingale claimed, there was nothing that could be done about scarlet fever deaths. By 1887 he knew he had been wrong, and altered the record of what he had written. Nightingale had shadowed him throughout his career, obstructing his attempts to divert public health funds from sanitation projects into scientific research.
So by the tail end of the 19th century there was a consensus forming about the importance of sanitation in controlling the disease, and handwashing (at least in a medical setting) was very much a part of that. How long that took to filter through to wider public consciousness, or what the public health campaigns looked like, I do not know.