Any surgery that was taken place before the 19th century was considerably risky. There was no anti-septic sterilisation process, penicillin was still to be discovered, and as a result many patients had a high risk of dying from infection after any operation. Therefore the circumstances which surrounded someone having an operation was pretty much a last resort.

Surgery itself wasn't even a defined profession until the 19th century, up until such a time the local barber was also your surgeon should you require any operation. You would most likely have been either given copious amounts of alcohol and given something to bite on. It's also quite likely many people would eventually pass out from the pain.

Source: GCSE History classes

Surgery in Great Britain during the 18th and 19th century was a tricky thing indeed. For centuries, there had been two basic types of medical practitioners: physicians and surgeons. Physicians were the first point of contact for the sick and often advised on a course of treatment. They were also typically university educated and were licensed by the Royal College of Physicians to practice medicine throughout the United Kingdom. Physicians also had several related professionals who would help them carry out their instructions. Apothecaries focused on stocking and mixing medicine. Nurses provided palliative care. Midwives specialized in delivering children. Surgeons merely amputated or cauterized their patients.

Surgeons had never been considered to be of the same class as doctors. Most early surgeons were also barbers and were paid for their ability to perform an amputation quickly and efficiently: no one wanted to be carved up over the course of several minutes. Surgeons were therefore paid for the speed at which they could perform amputations rather than the skill at which they conducted them. This led to the famous quip that Robert Liston was the only person in history to achieve a 300% mortality rate during the course of one operation: while amputating the leg of a patient, Liston also cut off the fingers of his assistant and slashed the torso of a spectator. All three later died in the hospital of gangrene.

There had been considerable attempts at developing anesthetics, although most of this consisted of opium, liquor and other common drugs. Laughing gas had been isolated as early as the 18th century, but it was banned in Britain due to its abuse as a narcotic by members of the upper class who held parties consuming the substance in drawing rooms throughout London. By 1850, both ether and laughing gas were beginning to be used for surgery, thereby allowing surgeons to refine their skills although the mortality rate was still considerably high.

Patients were typically strapped or held down to a table while the surgeon got to work. Naval vessels of the period carried limited stocks of medical supplies but the business of working in the Navy was treacherous enough that malaria and scurvy had a better chance of killing you before gangrene did, thereby making such preparations rather moot. Similar procedures were implemented on land. Since surgery carried such a high chance of mortality, however, it was often seen as a last resort.

A fascinating read on the subject of surgery in the 18th century and leading into the 19th is The Knife Man by Wendy Moore.