Web

To cast a video from your web browser, you should 

-use https://app.put.io on Chrome, and
-make sure that your device and Chromecast are connected to the same network.

When these conditions are met, you should see a Chromecast option in the menu next to the video:

iOS

As long as your iOS device and Chromecast are connected to the same network, you'll see a Chromecast icon on the top right corner. Here's a gif that shows it all clearly:

Did this answer your question?