The watched/unwatched, view progress, and ratings are stored in an install-independent fashion that makes them easy to move between installations or servers.
In order to do so, you'll need to use SQLite commands. These are built in to OS X, but you may need to install support for other operating systems.
Related Page: SQLite
Before you do anything, make sure that the Plex Media Server is not actively running on either the source or destination install.
The main Plex Media Server database is com.plexapp.plugins.library.db and its location will vary by operating system.
On Windows, the database is located inside of the user directory.
%LOCALAPPDATA%\Plex Media Server\Plug-in Support\Databases\
Using the Finder's "Go" menu, select Go To Folder... then enter the following in the dialog box that pops up:
~/Library/Application Support/Plex Media Server/Plug-in Support/Databases/
In general, the location for the various Linux versions of Plex Media Server will be found under:
$PLEX_HOME/Library/Application Support/Plex Media Server/Plug-in Support/Databases/
The following example commands are run from the command-line when in the directory noted above.
On your source Plex Media Server installation, export from the old database:
echo ".dump metadata_item_settings" | sqlite3 com.plexapp.plugins.library.db | grep -v TABLE | grep -v INDEX > settings.sql
Copy the settings.sql file you created to the new installation. On that new installation, add the data to the new database:
cat settings.sql | sqlite3 com.plexapp.plugins.library.db