I was reading about Henry V's injury at the Battle of Shrewsbury in which he was hit in the face by an arrow, and one particular thing in the ensuing surgery surprised me; the surgeon, John Bradmore, cleaned the wound with alcohol and honey. Considering this took place in the 15th century, how did surgeons know to use such items (that we know today have antibacterial properties) when they were not remotely aware of even the concept of bacteria? Was this kind of treatment for a wound standard practice?
Honey is an incredibly old treatment for wounds. It is mentioned in the Edwin Smith papyrus as a treatment for a cervical spinal wound (in case 30), dating to roughly 2500 BCE:
Title Treatment instructions for a wrenching / sprain in the vertebral column of the back of his neck.
Examination If you should examine a man for a wrenching/sprain in the vertebral column of the back of his neck, then you are to say to him: “Look towards both your shoulders and your chest”. When he does so, the ‘looking’ he is capable of, is painful.
Diagnosis Then you are to say to him: “one who suffers from a wrenching/sprain in the vertebral column of the back of his neck (this is) a medical condition I can heal”.
Treatment You have to bind it over fresh meat the first day. Afterward, you should treat with (powdered) alum and honey every day until he recovers.
Explanation As for ‘the wrenching/sprain’, he says about the wrenching apart in intervertebral joints: “Each vertebra is (still) in its place”.
Honey is apparently one of the most mentioned medications in the Hippocratic corpus by people who count these things. In any event, it was a widely accepted part of the materia medica, both for wounds and gastrointestinal disorders.
All of this is to say, by the time the 15th century rolled around, the use of honey was widely accepted.
How did doctors know? This gets down to much more fundamental issues in medicine (that I've written about before, because I'm crazy about this stuff) about how do we truly KNOW if a treatment works. In the case of something like a wound dressing, where there are tons of variables and a long course with a variable natural history, it's incredibly difficult to truly "know" whether a treatment works without running an experiment -- ideally a randomized controlled trial. No one knew to do this in the 15th century. Rather, doctors dealt with inherited knowledge, which was based on the study of classics. This was supplemented with practical (or experiential) knowledge. John Bradmore, who seems to have been a barber-surgeon, likely didn't have much study of Galen or Avicenna under his belt, but likely had treated plenty of wounds with a variety of material, and talked to other surgeons who had done the same. And believe it or not, this is remarkably similar to how much medical knowledge is passed down these days.
I used honey as an example, because some people have argued that the first actual medical trial was done by Ambroise Pare, who compared Egyptiacum (the salve of alum and honey mentioned in the Edwin Smith papyrus) to his beloved puppy oil balm (which is as horrifying as it sounds -- I won't describe it here, just google it). The salve worked better. (for the record, I'm with the majority in considering James Lind to be the progenitor of the clinical trial, flawed as it was, because of the fundamental innovation of randomization).
TL;DR: doctors knew because of inherited knowledge and practical experience. And given honey's prominence in the materia medica, and the fact that Pare used it as the comparitor in his medical trial, it does appear to have been a common treatment on wounds.
EDIT: I would also argue that you don't really need to understand transmission of a disease to effectively treat it. I mentioned James Lind above. The cure for scurvy was understood almost 150 years before we knew the cause. Similarly, quinine was being used to treat malaria over 100 years before the plasmodium spp was discovered. What you DO need, however, is some way to verify a treatment works -- a medical trial.