Ancient Medicine
There are really three branches of medicine in antiquity and through the Middle Ages. One of these might be called "doctor medicine," or "scientific medicine," where people try to observe sicknesses and look for logical patterns and figure out how the human body works and from there figure out what treatments might work. This kind of medicine really started with the Greeks, and the Romans went on with it, and it was very highly developed under the Islamic Empire. It is very organized and nowadays it is successful, but in the ancient world this theoretical approach probably did not cure very many patients.
A second kind of medicine might be called "natural cures," or "folk medicine", where less educated and less intellectual people try to cure sicknesses with various herbs like pennyroyal or valerian, such as you find in health food stores today. These people are also using observation and logic, but they are not so aware of it. On the other hand, they probably had more success in antiquity than the scientific doctors did. They tried things until they found something that seemed to work, and then they kept doing that. This kind of medicine probably goes back to the Stone Age, and after weakening some in the Roman Empire, became very strong again in the Middle Ages. The Islamic doctors took over some of these natural cures and brought them into scientific medicine.
Jesus healing a paralyzed man
from a Late Roman mosaic
Other times, a magician might make you a magic charm, or say a spell, to cure you (usually you would have to pay for this).
Some religious groups organized special healing shrines, that people went to when they were sick. People would often live there until they got better (or until they died). In these places people rested, got plenty of sleep, ate healthy food, drank water instead of wine, and exercised in various ways. Sometimes you took special baths in natural hot springs. You also talked to the priests and priestesses (or monks and nuns) at the shrine, who may have acted a lot like counselors or therapists today. If you were suffering from depression or you were just overweight or you had been working too hard, these places might be just the thing to have you feeling a lot better soon.

