The first European to come to Florida was Juan Ponce de Leon, who is thought to have landed someplace near Saint Augustine in the early 16th Century.  The Spanish explorer claimed the territory for his native country, naming the land after Pascua de Florida, the Spanish Easter Celebration.  Early colonization attempts by Leon failed mainly because of attacks by the area's indigenous people and diseases, both of which killed many of his men.  Eventually Spain was able to colonize Florida, as well as much of the Southern part of the United States, territory they held until the British took over part of the area in the 1700's. 

Florida was still largely populated by its native people, the Seminoles, well into the 18th Century.  As the the area became more and more popular for white settlers to move into, President Andrew Jackson began a program to have the Seminoles removed, spending millions of dollars and costing many lives, both white and native. 

In 1845 Florida became the 27th state in the US, with a population of about 90,000 people.  Today the state is home to millions and has a diverse economy based on tourism, agriculture, and technology industries.      

A good resource about Florida government and history can be seen here.