Incarcerated? Isolated from Process Servers? Not the case. Few of the Florida Statutes are as clear and brief on any topic. Florida Statutes have a 10-word response to how to serve process on someone that is incarcerated. (State Prisoners)
48.051 Service on state prisoners.—Process against a state prisoner shall be served on the prisoner.
So the simple answer is if you need to serve someone that is presently in State prison it is no different, legally than serving someone papers on the street.
Of course, there are differences in how it is done though. There are multiple layers of security in prisons, penitentiaries, and jails to maintain safety for those working in the incarceration facility, and for the inmates.
Service of process on those incarcerated involves a layer of conversation between those managing the prison (ie. the warden, or sheriff, or…) so that the service is done safely, timely, and with a minimum of disruption to the routine of the facility.
There is often a level of risk in the business of process serving. Not all people welcome being told that they are to appear in court. Oddly enough, service of process on an inmate, because of the safety protocols in place in these facilities, might be more arduous from a paperwork perspective, however, it is one of the safer places for a process server to serve papers.