Spanish colonization of the New World began in response to seeing the success of Portugal. As the Portuguese sailors were exploring the world beyond Europe, the Spanish sent out Christopher Columbus in 1492 to find a way to Asia. His journeys were followed by many more, each one claiming new land for the Spanish, until the 1500s, when Spain was in control of the largest overseas empire on the globe.
Source: Spanish Empire Anachronous 0, Trasamundo, Wikimedia
The Spanish were motivated by the 3 G's for colonization: Glory, Gold, and God. They hoped to become rich off the gold and silver that was being found in the colonies. They wanted to bring glory and power to Spain, especially since during this time period land = power. Lastly, they wanted to spread Catholicism around the globe. The majority of the Spanish colonies were located in Central and South America. The colonies were successful in bringing riches to Spain, partly due to the overwhelming success of the Spanish Conquistadors in securing land and subduing indigenous peoples whom they pushed off the land to use it for their own purposes, and in their use of slave labor. Eventually, Spain lost control of their colonies, as they began to fight for independence.