Torrents are not downloaded
If TVShows did not download any torrent even when new episodes have been released, you may need to check several things.
The Pirate Bay is blocked
TVShows retrieves most of its torrents from The Pirate Bay. Sadly, some countries and ISPs block that website. To see if that is your case, try to visit The Pirate Bay from your browser. If you can, then this is not the problem.
If you cannot access The Pirate Bay, TVShows can still work by using an alternative. Go to the TVShows preferences and check the Prioritize Magnet Links option. From now on, torrents should be downloaded correctly, try opening a show and manually downloading an episode.
A firewall is installed (e.g. Little Snitch)
If you have a firewall installed, you have to give both System Preferences.app and TVShowsHelper.app access to the Internet.
No menubar icon
If after a clean install you cannot see the menubar icon, there may be a problem with the permissions. Open the Terminal.app (under /Applications/Utilities) and write this if you installed TVShows only for your user:
xattr -d com.apple.quarantine
Or this if you installed it for every user:
sudo xattr -d com.apple.quarantine
After that just reopen the preference pane and the icon should appear. If so, your episodes will start downloading!
I see the menubar icon, but it's useless
A common issue is that maybe you set the save location to an external disk, and now the save location is not accesible. Just choose another location to see if that works.
Torrent files are downloaded, but not initiated
Go to the download folder you specified in TVShows preferences. Do you see some .torrent files? If so, maybe you need to configure your torrent downloader. Transmission is the best option, so install it if you do not have any torrent downloader in your Mac.
Then you need to make sure that the Automatically open each Torrent file after download option is selected in TVShows preferences. To get the best experience, go to the Transmission preferences and check/uncheck the following options: