Under normal circumstances, Floridians and all other U.S. citizens may renew their passports by mail. But not everyone gets off so easy. You have to apply in person if your previous passport was issued when you were younger than 16, if it was issued more than 15 years ago, if it's missing or damaged, or if you changed your name and can't provide supporting documentation. Also, if you need a passport in less than two weeks for international travel, applying in person at a Passport Agency is the only way (Florida has one, in Miami). Otherwise, Florida has numerous locations where you can renew your passport in person. It'll be mailed to you four to six weeks, or in two to three if you pay for expedited processing.
Visit the U.S. Department of State website to download and complete a DS-11 passport application. Either fill it out online and then print it, or, if you're more old-school, print a blank copy and fill it out by hand. Don't sign it, though, as this has to be done in front if the attending passport agent.
Figure out where you're going to apply in person. The U.S. Department of State website has a handy tool called the Passport Acceptance Facility Search Page. Simply enter your zip code or your city and Florida into the appropriate fields, click "Search," and get a list of nearby locations.
If you need your passport in under two weeks and are in or around Miami (or you feel like taking a road trip), make an appointment at the Miami Passport Agency by calling (877) 487-2778. It's located at the Claude Pepper Federal Building at 51 Southwest 1st Ave., Miami, FL 3313.
Bring the Form DS-11 to your chosen passport acceptance facility. Also bring along proof of U.S. citizenship, a government-issued identification, and a new passport photo. Details about which documents are acceptable and the required photo specs are on the Department of State website.
Pay the applicable passport fees. They vary based on which passport format(s) you get and whether you're paying for expedited delivery, but typically range from $30 for just a passport card all the way up to about $200 for a passport book and card with rushed processing. Detaile fee information is posted on the Department of State website. Different passport acceptance facilities take different forms of payment, so call your location ahead and ask how you can pay. Checks and money orders payable to "U.S. Department of State" are a reliable method, but most facilities also take cash and credit/debit cards.