How did spain establish territorial claims in the caribbean and south america?

Spanish colonization of the Americas - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Spanish_colonization_of_the_Americas)
History of THE SPANISH EMPIRE (http://www.historyworld.net/wrldhis/PlainTextHistories.asp?historyid=ab49)

History of the Spanish Empire from beginning to end (http://mn.essortment.com/historyspanish_rrbw.htm)