When and how did humans begin to discover how to control bacteria and viruses?

Answer 1

It was not so long ago that people realized that microbes even existed. Anton van Leeuwenhoek was the first person to see bacteria during the 1660s. He had ground magnifying lenses and was interested that he could see small microbes. For almost two centuries, the knowledge was regarded as an interesting but rather irrelevant fact.

The germ theory of disease was not really fully developed until the 1870s but, 30 years before this, a doctor in Vienna called Ignaz Semmelweis noted a disease called child-bed fever was passed from one mother to another by doctors not washing their hands.

Louis Pasteur and Robert Koch in the 1860s and 1870s finalized the Germ Theory of Disease. Both realized that boiling broth and covering it tightly kept out spoiling microbes.

You have to see that this was only about 140 years ago. Antibiotics were only available since the 1940's (Penicillin).

As for viruses, they were first discovered later as they are so small. Beijerinck investigated the cause of tobacco mosaic virus in the late 1800's but he could not see them but did prove something smaller than a bacteria caused this TMV.