Depending on the media, there are different ways to delete items downloaded from iTunes from an Apple device. To delete music and audio books, swipe left on the media you wish to get rid of and press the delete button.
To delete videos such as movies, shows, and music videos, navigate to the shows or movies and press edit. Tap the X that appears on the video that you wish to delete. This process is the same for deleting podcasts. To delete individual episodes of a podcast or show, select the show and swipe left on the episode to reveal the delete button, and press delete.
To delete apps downloaded from iTunes, navigate to the home screen and hold down the app that needs to be deleted. Wait until it jiggles, then press the X that appears on top to delete it.
To delete books or other reading material, navigate to the iBooks app or the Newsstand app and press and hold the media icon until it jiggles. Press the X button that appears to delete it.