When you first setup Chromecast you need to download the Chromecast app for iPhone. Tap "App Store."

Note: Also, be sure the Chromecast is plugged into an electrical socket and connected to a HDMI port on the TV.
Chromecast for iPhone -What is Chromecast? Chromecast is a media streaming device that plugs into the HDMI port on your TV. Simply use your mobile device and the TV you already own to cast your favorite TV shows, movies, music, sports, games and more.Chromecast works with iPhone, iPad, Android phone and tablet, Mac and Windows laptop, and Chromebook.