The campaign files will come in a zipped file. Just copy these files into Program Files (x86)\EA GAMES\Battlefield 2\mods\ folder.
Choose 'Extract Here' and let it install the files. Let it overwrite any files if you have older campaign files installed.
If you use the standalone version of the game, then copy the files into Program Files (x86)\FH2\mods instead and then extract.
Make sure to backup your cmp_minimod folder
before running the test updater if you want to play public
(it's in the levels folder inside the fh2 folder)