The best way to keep up-to-date with your favorite shows is to add them to My Shows. To do this, go to the show page and tap the "Add to My Shows" button.
Once you've added to your shows you'll have the option of turning on notifications so you can receive alerts when new episodes are released.
If you decide you don't want to turn on notifications, you'll still see when new episodes are released by checking in on your My Shows and looking for the blue dot on the show art.