Experiencing physical pain
According to my teacher, the enlightened attitude is to see pain is information. (For comparison, the non-enlightened attitude is to block/avoid/suppress pain by all means.) Because pain is information, we should evaluate it, see what message it carries and what it means for us, and then act.

Some physical pain is a symptom of a deeper-lying problem, and instead of suppressing the symptom a wiser approach would be to take care of the causes (often, bad lifestyle habits).

Some physical pain accompanies exercises that help one get stronger physically and emotionally. The right attitude to such pain is to accept the physical component and by accepting it eliminate the emotional component that comes from resistance and self-pity (so called "pain of pain").

Obviously, some physical pain is a sign of damage being done to the body right now, like the pain that accompanies tearing of ligaments. There is also residual pain that accompanies recovery process etc. -- these fall in the realm of regular medicine.

So the rule of thumb is to not worry about the pain itself, but the message behind it.

However, if pain is so overwhelmingly strong that it obscures the mind, I would imagine the Buddhist approach would not disagree with using anesthetics temporarily.