There is no "move database" command (that I'm aware of) in Firebird.
You'll need to move the databsse manually. There is however a method to do it in code and safely. You can backup the database to the same name but with extension .fbk (instead of .fdb for example). Then you can change the connection-string to include the new path and restore the backupped database.fbk to that location. At that point you have the database at the new location. There is however no possibility to delete the old database file.
All this is because you might not have physical access to the real database location. If you do have access you can delete the original database with a simple deletefile command. (you can also delete the .fbk backup-file when you're sure the new database is all correct)
For some code to backup and restore you can look at the wiki here:
http://wiki.freepascal.org/TFBAdmin