If a Florida resident files for divorce... how is an out-of-state respondent served...how does the process work? Is it even possible?
The easiest way is to hire a local process server, who will contract to an out-of-state process server. It costs about $100 for most states.
You can have the local sheriff's office serve the out-of-state spouse. Call the proper county sheriff and ask for the Civil Department. They will be able to tell you how much they charge to serve the papers.
Use a local server, they will outsource it to an out of state server.