This aspect of it is fairly easy to observe from inside the game; the Health screen goes on for three pages of possible symptoms, diagnoses, treatments, etc. This is just an overview, arranged like a spreadsheet with a row for each dwarf (and their pets and livestock) and a column for each symptom and so on.
It also tracks nerves and blood flow in a generalized way; any strike which penetrates or cuts the tissue layers has a chance of damaging the nerves in that body part. Nerve damage may or may not heal with the rest of the wound, and that will cause chronic infirmity or paralysis. Blood loss can cause dizziness or loss of consciousness, etc.
The combat logs are quite thorough, and after your first combat (which includes hunting and sparring) you'll quickly see how each actor is choosing from a "menu" of possibilities that varies from moment to moment. If one combatant loses a hand, they won't be able to strike with it, and nobody else will be able to target it with an attack.
If you then play the Adventurer mode, which is part of the same game but played as an individual character's perspective, you can see those menus reified as actual menus for you to choose from. Some of them are generic: you can swing your sword with or without targeting a specific body part. Others are much more specific. If your weapon gets stuck inside your opponent, you have the option of twisting it to cause pain (and probably more nerve damage).
In one game I played I fought a megabeast which had some kind of contaminated blood. My dwarves won the fight, but tracked the blood all over my fortress. I had them cleaning it up, but couldn't keep on top of it; eventually it was everywhere. A while later I noticed that a significant fraction of my dwarves and animals had rotting wounds on their feet...
The development log (http://www.bay12games.com/dwarves/index.html) and the game data files (which are all just text) also supply a lot of information, but they're not required reading; all of these details are pretty visible in the game. This is one of the things that makes the game so rewarding. Even when you lose a fort you can figure out what happened, and you can figure out how to avoid it or solve it next time.