Northern Florida is much cooler in winter than southern Florida, so pack a heavy sweater or more. Even in summer, ocean breezes can be cool, so it's good to have a lightweight sweater or jacket.
Aside from an occasional winter cold spell (when the mercury drops to, say, 50), Miami and the Naples–Fort Myers areas are usually warm year-round and extremely humid in summer. Be prepared for sudden storms all over in summer, and note that plastic raincoats are uncomfortable in the high humidity. Often, storms are quick, often in the afternoons, and the sun comes back in no time. (This also means that it's best to get in your beach time earlier in the day; if it's nice in the morning in August, go to the beach. Don't wait.)
Dress is casual throughout the state—sundresses, sandals, or walking shorts are appropriate. Palm Beach is more polos and pearls, Miami is designer jeans, and elsewhere the Tommy Bahama–esque look dominates. Even beach gear is OK at a lot of places, but just make sure you’ve got a proper outfit on (shirt, shorts, and shoes). A very small number of restaurants request that men wear jackets and ties, but most don’t. Where there are dress codes, they tend to be fully adhered to. Take note that the strictest places are golf and tennis clubs. Many ask that you wear whites or at least special sport shoes and attire. Be prepared for air-conditioning working in overdrive anywhere you go.
You can generally swim year-round in peninsular Florida from about New Smyrna Beach south on the Atlantic coast and from Tarpon Springs south on the Gulf Coast. Bring a sun hat and sunscreen.