As from this comment on a recent question, I was wondering - Columbus' expedition was viewed as idiotic. The consensus opinion would have been that he was going to die, because of the sheer distance involved, right? So how did he convince people to sail with him? What crew would sign on to a ship that was on a journey that was not only possibly going to end in disaster (as per the regular risk of wooden sailing), but that they would have believed to be in fact guaranteed?
What about other explorers? How did they convince crews to go on expeditions that had serious risk of ending in failure, when the price of failure was most likely death?
As per some discussions in the linked post, the Columbus expedition was not considered so 'idiotic' as you make it out to be. It could be considered foolish, unlikely to succeed and quite dangerous but probably not 'guaranteed to end in disaster' or anything of such deterministic apocalyptic tones.
It is important to note that Columbus proposal was not to sail non-stop however it takes until reaching land, but in fact bounded by some estimates on how far and how long it will take - he claimed the desired destination was 750 - 1000 leagues away from Europe. If he didn't reach it by that distance/time, the crew would force him to turn back, and indeed the pressure and unrest had already started manifesting itself when the first islands were spotted.
Columbus did have some problems in organizing his expedition, as he was welcomed with interest and enthusiasm by some, and unwillingness and skepticism by others. To succeeded in his organization the Monarchs gave him various grants most important were direct orders to the town of Palos to provide him two caravels in their cost (to settle an old debt) and give him all assistance. It seems he did find enough volunteers, but he seems to be aided in this by the Pinzon brothers, local ship owners, who decided to back his expedition. I would call /u/TywinDeVillena to give more insight about the local Andalusian support or lack of one.
Still, grudges and unwillingness remained with at least parts of Columbus crew, as for example Columbus notes early in his log that he suspects the problems with the rudder of Pinta that befallen them immediatly after leaving was caused by some sabotage by some unhappy crewmen.
All together, part payment of wages, part pressure from the Royals, part idea of possibility of success was what gave him support. In general though, none of the crew would sail to certain death, and they were more then prepared to turn the ships around when deciding enough was enough. Columbus was not really at the point of no return yet when he reached the new lands, yet was approaching it fast