Google itself has an official Android TV remote app for iPhone, iPad, and Android devices. Related: What's the Difference between Google TV and Android TV? These will allow you to navigate around the TV's apps and menus. The Chromecast with Google TV is also an Android TV device at its core, which means it can be controlled by a 'remote' app on your phone or tablet.
You can 'cast' videos and music to it from your phone or tablet. First of all, as the name implies, the Chromecast with Google TV is a Chromecast device. If you don't have the remote or would rather use your phone, there are a couple of options.