How did the Crusades lead to the discovery of the New World?

The Crusades were a series of military expeditions in the 11th, 12th, and 13th centuries. European Christians believed it their duty to recapture the Holy Land from the growing Muslim Ottoman Empire. By the end of this pursuit, many Crusaders had returned home with exotic goods like spices, silks, and gold they had acquired in the Holy Land. With a hunger for these exotic goods from as far off as China and the Indian subcontinent, European nations began seeking a quicker, cheaper route for getting their hands on what they wanted. 
When the Crusades ended in the 13th century, trade for exotic goods did not entirely come to a halt. Rather, the flow of goods had to pass through many hands, over many miles of land and sea, before being traded from Muslim merchants to Italian merchants, and from Italy to the rest of Europe. With each trade being made, prices went up! Imagine the poor people of Britain who just wanted a little pepper for their soup! 
In response to this high-demand, high-price situation, the Portuguese established a navigation school and quickly became the major players in European exploration and trade. The Portuguese were the first to round the tip of Africa and find a sea passage to India, where silver, spices, and textiles could be acquired. They were also the first to reach Southeast Asia, and second in the New World. Before the Portuguese, the Italian sailor Christopher Columbus sailed to the New World on behalf of Spain.
When Columbus made his fateful voyage in 1492, he wasn't looking for a "new world" or Biblical paradise... he was seeking a sea route to Asia to the west! He believed that Spain could get a leg up on Portugal by going across the Atlantic rather than around Africa. Of course, where he landed was not India or China at all, but the Americas. There he and other explorers found resources they already knew to be valuable (gold and gems) as well as new luxuries to be exported (tobacco, chocolate, potatoes.) European desire to have exotic goods at reasonable prices, combined with a sense of duty to spread Christianity- which served as an excellent tool for justifying Colonialism- the Americas were rapidly conceptualized as a land of resources waiting to be shipped across the Atlantic.
https://www.britannica.com/event/Crusades

https://www.britannica.com/topic/European-exploration