How do I watch free tv shows on my iPhone from iTunes

Have you searched the iTunes store for free TV shows. You can sometimes find the first episode of a series that's been made available free of charge as an inducement to get you interested so you'll buy the series. Beyond that, you're not going to find much in the way of "free TV" in iTunes.

This is the first I have heard of the iTunes Store offering free TV shows.

Unfortunately, iTunes does not offer free TV Shows. But sometimes there will be some that will go on sale. Go onto the Apple website to opt in to get emails on the latest releases and more!