The original NWA came together in 1948. For most of its long run it was headquartered in St. Louis. It divided the country into territories as well as Canada (Mexico was one big territory and Japan was a bit different I believe) They recognized one World Champion one Jr. Heavyweight Champion and the promoters who were part of the NWA voted on who those champions would be. The territories were free to recognize whatever other champions they wanted.
While they'll say the AWA and WWWF split from the NWA, they really did not. They semi-split in exchange for having their own champion but they still basically followed the NWA rules about not entering territories that another promoter had (but if they died, Verne especially would grab what he could)
When Sam Muchnick finally retired, the NWA started to split apart with Crockett grabbing most of the power and basically dictating champions. Shortly after, Vincent K. decided to stop following the NWA rules and started to expand the now WWF and from there, the NWA started its downward spiral till its first death.
During the NWA's time, the World Champion would tour an area for a week or two, work out angles against their top guys, set up stuff for feuds in the fed, wrestle a couple matches and then move on to the next territory.