First of all, there is a great thread for further reading on Florida History: http://www.freerepublic.com/focus/f-news/993896/posts
Florida raised the greatest number of troops per capita during the WBTS. She was the third state to seceed, with close ties to South Carolina. In fact, many thought the hostilities would erupt at Ft. Pickens rather than Ft. Sumpter.
Florida itself did not have many battles in state. Two that come to mind were Confederate victories - the students in Tally held Union troops outside of the city in the battle of Natural Bridge. The battle of Olustee had the greys overwhelming the blues at Lake City (which is now home to the world's largest CBF).
The Confederacy counted on Jake Summerlin and the "Cow Cavalry" to supply beef and salt to troops in VA, MS, SC, etc. Floridians engineered the first desalinisation (??? I mean no salt) plants on the ocean, but were often forced to abandon their stills in the face of attacks.
The famous blockade runners made the trip up the St. John's (going South) to Sanford, hiked thru Melonville, Geneva, and New Smyrna or Mosquito Lagoon to make the run to the Bahamas for trade (sugar and rum).
I found a quick history of Florida in the WBTS here
I'm currently reading "Confederate Florida" and I can recommend "Florida in the Civil War" by Nulty as a quick and comprehensive book of the subject.