A popular website for downloading Persian subtitles for movies and TV shows is subscene.com. Once on the site, enter the name of your show of interest in the search bar. The first column in the results specifies the language of the subtitle file. Look for ones that are in "Farsi/Persian."
There might be more than one file matching your search criteria. In that case, pick any of the files and download it on your computer. Copy the file to the folder that contains the video file that you want to play. Change the name of the subtitle file to match the name of the video file. Play the video file and check if the subtitles appear. If they don't appear, are out of sync or look disrupted, try downloading another subtitle file and repeat the procedure.
Another website for downloading Persian subtitles is farsisubtitle.com. The entire website is in Farsi and it only has Persian subtitles in its database. You can browse through categories or search for a specific title to find the subtitles for the movie or show that you want to watch.
If you can't see any subtitles at all when playing your video, it is possible that your media player can't display subtitles. The VLC media player, which is available for download freely at videolan.org for both Windows and Macintosh as of August 2015, can display subtitles seamlessly.