To become a public defender you have to first become a lawyer.
To become a lawyer in Florida you have to obtain a 4 year bachelors degree in some course of study, preferably social sciences of some kind. Then you take a law school entrance exam call the LSAT. If you receive a high enough score you apply to various law schools for admission. Once admitted to a law school you study law for 3 years or so in order to receive your degree in law call a Juris Doctorate.
After graduating from law school you are required to take a set of exams given by the Florida Bar to determine whether you learned enough law in law school to be admitted to practice law in Florida. But it isn't enough just to pass the bar exams, you will also be screened for character. People who have arrest records or mental or substance abuse problems will usually not be admitted to the bar. So don't get into any trouble on your road to becoming a lawyer. If you pass the bar exams and the screening, you will then be sworn in to practice law by the Florida Supreme Court. You are a lawyer.
Next, you have to apply for a job at a public defender office.
I believe the associates degree in liberal arts offered by Polk State College is your first step. There will be guidance counselors there at Polk State College. Find one and tell him/her what you are trying to do. Talk to people there and get as much information as possible. Be prepared to study hard and to dedicate the next 7 or so years of your life to your dream. It's not as hard as it sounds. Its done all the time by young people like you. And when you are sworn in don't lose your idealism. Ours is a service profession, make it proud of you.
Good luck and God bless.
Everything the other lawyer stated is accurate, but I will offer a different opinion about what to major in. Typical pre-law majors are political science/history oriented. If you had said you wanted to be a politician, then I'd say that makes sense. Otherwise, none of that cocktail party kind of trivia made a difference in my life on the LSAT, in law school, or in the courtroom. You want to leave college capable of being a good writer, having good reading comprehension, but most importantly, with the ability to think logically and be competent in analytical reasoning. The skills you learn in mathematics and the hard physical sciences like physics, chemistry, computer programming are great ways to become good at logic and analytical reasoning. As a lawyer, rather than using numbers, you will be using the words in statutes and case law, and the facts in your cases to run through complex analyses. Not to mention most of the LSAT is logic and analytical reasoning for these very reasons. So even if you major in the typical "pre-law" stuff, don't shy away from calculus, chemistry, physics, or if your school offers it, a course in logic. And I can't say enough about picking up Spanish as second language if you want to be an attorney here in Florida.
Majoring in a category in undergrad such as criminal justice, political science, or even psychology is helpful but definitely not required. I know lawyers who have majored in tv production, math, art, etc. I would recommend trying to take a course or few in business law to get a flavor of what you'll need to learn in law school. To gain entrance into law school, you'll need your bachelor's degree along with a decent grade on the LSAT (I recommend taking a prep course for the LSAT, but note the LSAT is not remotely indicative of what you do in law school). To succeed in law school you must be determined and have decent reading comprehension skills along with common sense. Law school typically takes 3 years (full time) or you can take a 4 year part-time program (not all schools offer the 4 year course). After law school you need to pass the Bar Exam, pass an ethics exam, and pass the moral character portion of your application to become a member of the State Bar. During undergrad and law school I recommend trying to secure an internship or volunteering time for the court and/or offices of the Public Defender, District Attorney, City Attorney, or County Attorney. Be prepared to do a lot of tedious grunt work but you'll learn as you go. Good luck to you!