Windows/Mac: Most popular apps allow you to cast audio and video to your Chromecast directly from the app itself, but it's not supported by everything. Instead of just streaming from one specific app, you can stream all your computer's audio through your Chromecast for maximum support. On Windows, you need Chromecast Audio Stream. Once it's installed, just select your Chromecast from the tray icon and your audio will start streaming.
On Mac, you can use Soundcast. Here, you'll first need to install Soundflower, then install Soundcast (you might need to reboot after installing Soundflower). Then, select Soundcast from the menu bar, select your Chromecast, and you're all set.
That's it, now all your computer's audio should be routed through the Chromecast. This should work for everything from iTunes to video games to random MP3s you're playing from a folder.