So I have my first hospital finally setup (injured dwarves are fixed up rather quickly now, no matter what the injury). I'd like to share what/how to go about it for future newbs.
First thing is first. Ask your Dwarf Liasion/outpost trader for Gypsum Plaster (under powder). I have not found the right material to make it, and it's important for setting bones later.
If you have no ore, then also ask for some cheap metal (important for the chain for the traction bench).
Second, you need a Chief Medical Dwarf (n), create one from the Nobles menu. Enable all labors related to medical (I used Dwarf Therapist for this), disable all hauling and other industry related labors. It's also best to assign him to burrows that are within your fortress.
Third. Create a room, and put some beds in it. Zone (i) it as a hospital.
Fourth. Create a chain at a metalsmith's forge with some cheap metal. Then create a Traction Bench at a mechanics workshop.
Fifth, create a chest at a carpenter's shop, and a few buckets (more than one bucket is needed as dwarves use buckets for multiple purposes, one is needed for the ashery and one for the soap maker's shop).
Place the Traction Bench and chest inside the zoned hospital room.
Sixth, now for the hard part. Soap.
You're going to need a Butcher's Shop, a Kitchen, an Wood Furnace, an Ashery, and a Soap Maker's shop.
If you have a hunter. Ensure he has a quiver (made at a leatherworkers shop), bolts (craftdwarfs shop), and crossbow (bowyer's shop) so he can hunt for you some animals.
If no hunter is available, you can just butcher an animal (z).
Once the animal is being butchered at the Butchery, make sure you have someone with cooking enabled to render the fat at the kitchen.
While this is going on, have someone making ash at the wood furnace.
Once you have ash, have someone make lye from ash at the ashery.
Once you have all those ingredients, you can make soap at the soap maker's shop.
Seventh. Create some splints and crutches at the carpenter's shop (has your trader arrived with gypsum plaster yet?)
Eighth. I forgot to mention. Cloth. As I don't really know how to make cloth yet. I asked for it to be traded. I imagine it can be done from sheering an animal (Farmer's shop) and looming it into thread (at a loom shop). However, collecting enough wool from sheering takes a long time and I have no idea how to process plants into thread yet, as all my plants are considered rotten. However, it is manageable as you usually start with a fair amount of cloth.
Ninth: Update: For more advanced cleaning of wounds (I found I was still getting infections), one might need to setup a completely constructed cistern. Construct a simple outdoor cistern, which means walls, floors all have to be constructed. Then setup a screw pump to pump in water, then build a well on top. Set it as a water source. This way your dwarves have clean water (untested)
That's it. You now have a working hospital!