Review the statute and sunbiz.org. Don't forget the publication requirement. Also, you'll want a written action or corp. meeting to authorize said action, I imagine.
You need to do the following:
1) Search the sunbiz fictitious names to be sure yours is available. Even if another person is using the name you can use it as well, but you may run into trademark issues.
2) Draft a corporate resolution authorizing the DBA (check the bylaws - an officer may be able to do it without a resolution)
3) File online here: https://efile.sunbiz.org/ficregintro.html. But remember that you need to publicize the name in a newspaper in accordance with the information in that link.
4) Remember that you need to renew the filing every 5 years.