To deliver medicinial aid wherever aid is needed throughout the world, especially where human suffering is greatest.
To quote their website:
"We are Doctors Without Borders/Médecins Sans Frontières (MSF). We help people worldwide where the need is greatest, delivering emergency medical aid to people affected by conflict, epidemics, disasters, or exclusion from health care."
Doctors without Borders is comprised of a diverse range of both medical professionals, technicians, and administrators.
The organization is so large and diverse in its portfolio of accomplishments that it is hard to pinpoint through their research precisely how they approach disasters. However, their overall message is that they help where help is needed most and supply quality medical care for the people there. They seem to have a wholistic approach wherein they supply all care post-disaster instead of focusing on the immediate effects of the disaster.
It was a new way of addressing disaster in 1971 when it was founded.
“It’s simple really: go where the patients are. It seems obvious, but at the time it was a revolutionary concept because borders got in the way. It’s no coincidence that we called it ‘Médecins Sans Frontières.’”
The organization was founded because of the experience of volunteer Red Cross doctors. These doctors wanted to tell others what they had seen and to help bring more aid to those that are suffering.
Through grants and individual donations. Honestly I have no idea, I tried searching their financial documents but it didn't really tell me anything. They don't publish who donates to them.
They seem to support their approach by their own success.