Where
.local/share/7DaysToDie/Saves/<WorldName>/<GameName>/ holds the save (region files, player profiles, main.ttw). Random-gen worlds also need their terrain: .local/share/7DaysToDie/GeneratedWorlds/<WorldName>/. Both folders belong together.
From your PC
Windows: %appdata%\7DaysToDie\Saves\ and %appdata%\7DaysToDie\GeneratedWorlds\. Upload the matching <WorldName> folders to the two server paths, set GameWorld and GameName in serverconfig.xml to the same names, start. Player profiles in a local save are tied to your local Steam ID; on the dedicated server your character continues if the same Steam account joins.
From another host
Same two folders. Take serverconfig.xml too if you want the same settings; check the ports and passwords in it afterwards (the panel rewrites those anyway).
New world, keep the old
Change GameName (and/or WorldGenSeed) in serverconfig.xml. The server generates a new save; the old folders stay on disk. Switch back by restoring the old names.