The process for obtaining a contractor's license for painting can be summerized as:
1. Obtain a Specialty Business License from the Construction LIcensing Board.
2. Attend a minimum of 14 hours of training in construction codes and administration.
3. If you are a single proprietor ship who also paints, you will not need the spcialty business lincence.
4. Apply for the license and pay the fee.
You can find out more information at: http://www.myflorida.com/dbpr/pro/cilb/cilb_index.shtml
You can apply for the license at: https://www.myfloridalicense.com/Default.asp
Note that there is not a license for paiting per se. you would have to get a Contractors specialty license which covers you for particular phases of a construction project, etc.