It is generally believed that the Medieval Era was almost entirely ignorant of medical and surgical procedures.
This is simply not true.
By about 1400, medical knowledge included knowledge of the importance of cleanliness; suturing of wounds, blood vessels, and nerves; treatment of simple and compound (open) fractures, dislocations, amputation, cauterization to prevent excessive blood loss; anaesthesia; trepanning to treat skull fractures; gangrene and debridment of dead tissuel; etc. etc. Much of this knowledge dates to the Classical era, but some of it was developed during the late Middle Ages.
Medieval surgeons knew pretty much everything you need for battlefield medicine with the notable exception of antibiotics, transfusion, intravenous drips, and organ transplantation.
What does this mean? Well, if you can get to a surgeon and haven't lost too much blood, you're in OK shape. You might get an infection, and there's really nothing they could do about that, but if you don't (or if you survive it), you're likely to live.
Battle commanders of the Middle Ages were well aware of this fact. For instance, during the campaign that included Agincourt, the English army of 10,000 brought at least 24 surgeons - about one for every 400 men (incidentally, the current standard is about 1 surgeon for every 500-800 men).
By the 1200 or so, there were established medical schools you could go too, and the requirements for training were actually not that far from today's - you would take a 3-year college degree, a 4-year medical degree, then a year of practical study, and possibly another year of anatomy for surgeons.
The idea of getting your wounded Fighter to the Surgeon is definitely a lot less snappy than getting hands laid on by a Paladin or a Cure Light Wounds from a Cleric, but for a high-grit low/no-magic campaign set in a Middle Ages-like setting, consider having Surgeons available for hire in major centres to patch up serious injuries.
Regarding pricing, there's some evidence that medieval physicians and surgeons charged on a charge-what-you-can plan - i.e. make the wealthy pay through the nose, and give care away for free to the needy. So excellent medical care need not only be available to the wealthy.
Surgery will feature in my upcoming draft of a Descriptive Damage System, a gritty replacement for a hit point system that focuses more on roleplayable injuries and treatments.