According to the state of Florida, "anyone using or supervising the use of restricted use pesticides on agricultural or related sites" needs a license. If you are applying pesticides (including Roundup) to farms or large swaths of land from the ground or from the air, you should apply for a "restricted use pesticide license" (or RUP). If you are using it around your own private yard, you do not need a license, but you may consider putting up sign telling your neighbors' kids to stay off your lawn.
Decide which type of RUP you need. This will depend on your needs and where you intend to spray. A private license is valid for use on your own land or place of agricultural employment. A public license is valid for use at your place of employment if you work for the government. A commercial license is required for all other applications not explicitly covered in the private or public license descriptions.
Take the exams you'll need for your RUP license type. All license types must take and pass the "general standards (core)" exam, however, from there the exams you'll need to take depend on how you intend to use the license. Go to Florida's Agricultural Environmental Services' website for a list of the different exams you'll need to take in order to gain the proper license. The exams are given at your county's local Cooperative Extension Service offices.
Complete the license application that will be sent to you with the results of your exams, assuming you've passed. You'll also need to pay the license fee, which, as of 2010, is $100 for private and public licenses, and $250 for commercial licenses. Return the application with the fee to the address provided.