|18th-century trepanning kit|
It seems to me that if you want a low-tech but still basically effective medical system in your fantasy world, the single most important concept to give your characters is cleanliness. Basic personal hygiene and keeping wounds as clean as possible raises the survivability of life by a substantial margin. Antibiotics and such are great too, but this more basic hurdle tends to get forgotten -- even today. See all the talk about controlling pandemics with simple soap and water.
The importance of cleanliness isn't immediately obvious if you don't know about bacteria and viruses. Add to that the fact that for centuries bathing meant getting wet, getting wet meant getting cold and getting cold meant getting sick... and you can see why people didn't bathe much in northern Europe until recently. The most obvious connection for them was bathing = getting sick.
What about the smell? That's why we invented perfume. Plus, people smell. Nowadays, we've been programmed to believe human beings are supposed to smell like flowers/mint/soap/etc. at all times, not human beings, but that's a rant for another day.
Without a scientific basis, an emphasis on cleanliness (despite the risk mentioned above -- or can you eliminate the risk somehow?) will need to come from either religion or culture. An emphasis on purity in the society's religion, maybe? If you want a more general cultural reason to keep clean, think about practical incentives to be clean. Maybe there's a nasty bacteria in the local mud? The local blood-sucking bugs pester unwashed people more?
Low-tech medicine that is free of some of the long-running misconceptions (such as medicinal bloodletting) that plagued real-world medicine raises survivability too. On the other hand, such things can themselves be world-building elements.
Pardon me while I shoot down an example of this which has been bugging me for a long time.
"Cleansing" a wound with boiling-hot wine
I was a fan of Martin's Song of Fire and Ice series, but this point always rankled me. It's a prime example of counter-productive medicine and as such it makes a good world-building element. But let's review this concept, shall we?
The alcohol in wine is primarily ethanol, which boils at a temperature of 172(F)/78(C). However, the water in the wine boils at 212(F)/100(C). So if you heat it until the water in the wine is boiling -- because wine is maybe 12% alcohol, 88% water and that's modern wines, mind you -- your alcohol has been boiling off for some time already. If anything was going to kill bacteria in your wound, it was the alcohol.
So pouring hot wine on your wound adds a second-degree burn to your problems and kills the flesh around the wound -- making it more hospitable for bacteria and giving your body extra healing to do.
I blogged about more effective options over at Science In My Fiction: Part 1, Part 2 (discussing medical-grade alcohol)
How do the doctors in your world treat their patients?