Great question! There are many myths regarding Christopher Columbus and his voyage. For example, there is the the myth that sailors in the late 1400s still believed the world to be flat and if you sailed far enough, you could sail over the edge. By the time of Columbus's voyage, while the myth persisted in some sailor's minds, seasoned sailors had concluded this was not the case.
So, how did Columbus keep everyone onboard in this journey? One way was to constantly remind his crew they would be financially rewarded upon the discovery of gold and other valuable spices. For most sailors, exploration was not the primary reason they signed on to long and dangerous voyages.
However, as the logs of Christopher Columbus indicate, the dreadful unpredictable weather, low provisions, and lack of discovering riches quickly dissipated the initial enthusiasm of the voyage. At one point the crew threatened a mutiny! Columbus, recognizing the potential danger of the voyage ending prematurely, did something which probably many sea captains did during his time; he showed them his log and journal. What the crew didn't know was Columbus kept two logs. He kept one for show and the other an accurate record of his journey. This probably did not persuade everyone to continue the journey, but it was probably enough encouragement to mollify the crew wanting to return home.