One, Columbus and his crew knew the Earth was round. He was just wrong about the Earth's size. Columbus used Ptolemy's Geography and the Imago Mundi based on Muslim scholarship and ended up overestimating the size of Asia and underestimating the size of the oceans. Two, Columbus never thought he'd made it to China. He called the people he encountered Indians because he thought he'd made it to the East Indies, what we now know as Indonesia. And three, Columbus was not a lucky idiot. He navigated completely unknown waters primarily by using a technique known as dead reckoning in which you figure out your position based on three pieces of information.