They probably had a mixture of folklore about herbs and midwives like medieval
or early modern Europe. The did die in the Plague that decimated the
population of men, but other that that they seem to survive pretty well.
I don't think Middle Earth has many bacteria or viruses (other than Morgoth's
taint and the other Dark Lord's nasty stuff). Hopefully they don't use
leeches!
++++++++++++++++++++++++++++++++++++++++
"The world is changing: I feel it in the water, I feel it in the earth, I smell it in the air"
--Treebeard