Norman Davies Nevills was born in Chico, California, on April 8, 1909. He was the only child of William Eugene Nevills and Mae Davies Nevills. Norman's paternal grandfather, also named William but known as "Captain Billy" Nevills, had been a successful miner and promoter during the California gold rush of the 1850s who lost everything in the San Francisco earthquake of 1906. William E. Nevills was a prospector in Alaska before coming to Mexican Hat, Utah, in the 1920s. William was drawn by one of the periodic oil booms that were common in southeast Utah. After two years of college at the College of the Pacific, Norman joined his parents at Mexican Hat in 1928 to assist with the oil development work. The expected oil fields never materialized, however, (although Norman worked off and on at drilling for oil until his death), and the Nevills family was forced to turn to other means of making a living. They built a tourist lodge above the San Juan River, which flowed through town, and Norman began guiding parties of visitors by car through Monument Valley and other nearby attractions. In between times, he supplemented the family income by doing whatever odd jobs he could find. In 1932, Norman was asked by a miner to haul a load of supplies to a placer mine a few miles downriver, which he did successfully. From this beginning, Norman Nevills launched his river career.

In the summer of 1933, Norman participated in an archeological survey of the area around the San Juan river; part of the survey involved the use of folding canvas boats on the San Juan. On October 18 of that same year, Norman was married to Doris Drown, a native of Portland, Oregon. For their honeymoon trip, Norman decided to take Doris down the San Juan. He built a boat based on a design given to him by his father, who had hauled supplies and passengers on Alaskan rivers during the Klondike gold rush. Family legend has it that Norman built the boat with boards from a horse trough and an old outhouse, and used oil well suction rods with steel blades for oars. The trip, to Copper Canyon in February 1934, was a success. Two years later, knowledge of Nevills' experience on the river had spread sufficiently for a party from California to contact him and hire him to guide them down the river. This he did in March of 1936, and for every year after that until his death in 1949, Nevills led groups down the San Juan River on excursions throughout the summer months. These trips became his bread and butter, and often the receipts and deposits from the San Juan trips financed his other trips on the Green, the Snake and Salmon, and through the Grand Canyon.

Nevills' first major expedition and the beginnings of his subsequent fame as the number-one Whitewater man in America was in 1938. In the summer of that year he led three boats and a crew of two other boatmen and six passengers (including two women) from Green River, Utah, through Cataract Canyon and the Grand Canyon. Although internal dissensions threatened to end the expedition at Lees Ferry, the beginning of the Grand Canyon, Nevills and Elzada Clover, the co-organizer of the trip, were able to keep the party together and complete the trip. Nevills and Dr. Clover had planned to write a book about their experiences on the river, but this never materialized, and each went on to other things. Nevills' second major trip was in 1940. This time he ran almost the entire length of the Green River, from Green River, Wyoming, through the Grand Canyon. The crew included his wife Doris and another woman, and from Green River, Utah on, Barry Goldwater, later to become a powerful Western politician.

In 1941 and 1942, Nevills conducted private charter trips through the Grand Canyon, giving him a lasting place in Colorado River history as the first person to go through the Grand Canyon more than twice. On the later trip, Otis Marston was one of the passengers. Marston and Nevills were at first close friends, but later personality conflicts drove them apart and Marston became one of Nevills' most vocal detractors; this was to have great bearing on Nevills' reputation after his death. By the time the 1942 trip was over, the U.S. was involved in World War II, and Nevills nascent river outfitting business was considerably curtailed. Although he did conduct a few parties down the San Juan during the war years, most of his time was spent working for the U.S. Geological Survey, whom he joined as resident engineer at Mexican Hat in 1943. In 1945, with the war almost over, Nevills took a party that included Otis Marston and Ed Hudson (who had also been on the 1942 Grand Canyon trip), Marston's daughters and wife, and others, down Cataract Canyon of the Colorado. This marked the resumption of a pattern that Nevills held throughout the rest of his life: spring and early summer trips on the San Juan, and then a major expedition on another river later in the summer. In 1946, it was the Snake and Main Fork of the Salmon Rivers in Idaho; in 1947, 1948, and 1949, the Grand Canyon. In 1950 Nevills planned to try a river in Canada or perhaps Asia, but death intervened.

Throughout his career guiding parties on the rivers of the West, Nevills was supported by his wife Doris. Indeed, many who knew them say that Doris was a very real reason for his success. Doris organized all the menus, shuttles, and other logistical details that are absolutely essential for a successful commercial river trip. In addition, she smoothed over disputes and ruffled feelings among passengers and boatmen that were caused by Norman's often abrasive personality. Doris was by all accounts completely devoted to Norman, and endured with good spirit the verbal abuse that she reportedly received from Norman's mother Mae Nevills. Doris' support of Norman's chosen career extended to pawning her jewelry during the early lean years, before Norman became famous, and caring for their two daughters, Joan, born in 1936, and Sandra, born in 1941. The one thing that Doris reportedly did not share was Norman's passion for flying, even though the Piper J3 that Norman bought in 1946 was a great convenience, given their isolated home. It was in Norman's plane that they met their deaths together, when the plane crashed on takeoff at Mexican Hat, on the morning of September 19, 1949.

In today's high-tech and big-business world of commercial river running, where thousands of paying passengers are taken down river annually, and thousands of dollars spent on equipment and permits by outfitters, Nevills Expeditions, with its wooden boats and slim margin of profit, seems quaint, like something out of a forgotten era. Indeed, after his death, Nevills' reputation suffered at the hands of later rivermen, who said he was too cautious, too much of a showman, and so on. Undeniably, Nevills was a showman, and was concerned with his own reputation. Equally undeniably, however, is the fact that to Norman Nevills must be given the credit for a number of firsts (so important to boatmen!) on the Colorado. He was the first to run the Colorado through the Grand Canyon more than twice, the first to run a strictly commercial river trip through the Grand Canyon, the first to take women on commercial river trips, and the first to take women through the Grand Canyon, which was unheard of at the time. Nevills was the first to admit that he was a cautious boatman, but he also was proud of the fact that he never flipped a boat on all the rivers he ran, a safety record hardly matched today. His boat design, the Cataract boat, remained one of the standard river craft until well after the end of World War II; those who continued to use his style of boat did so long after others had converted to inflatable rubber boats. Nevills' principle of "face your danger" (i.e. the boatman faces the obstacle and rows away from it) is still the way rapids are run today, and although others had used the technique before him, he popularized the idea.

Norman Nevills was a pioneer, indeed one of the pioneers of commercial river running, and there are still companies operating today that can trace their roots directly back to Nevills Expeditions. Virtually everyone on the river today is there because Norman and Doris Nevills were willing to "face their danger."