There’s a few options to do so.
1. The 3rd party app
Download SonosTube, your Sonos speaker will appear in the app automatically if you are connected to the same WiFi obviously. Select the music you want to stream. Done.
2. The Youtube Premium way
Get YouTube Premium / Music, add your account in your Sonos controller and chose from YouTube music. This way you won’t need to use your phone. But you will not be able to play continuous streams like radio stations as this method only plays YouTube music.
3. Stream from your mobile with YouTube app running in the Background
You will need YouTube Premium or YouTube music. After activating YouTube premium your YouTube app will automatically activate a feature called “Background play” in your account settings. You will be able to stream YouTube even if the app is running in the background. Which is great because you do not want to always keep your phone open and unlocked. You can choose between always on or just if you have speakers or headphones connected. You choose the music or live stream you want and choose air play. Turn off you screen after you started the stream and the music will still continue to play in the background.
In general it would be nice to add continuous streams directly on the Sonos controller. Like this you would not need a phone to listen to your favourite stream. But there seems to be some kind of a problem with that as continuous streams do appear in the Sonos controller app but cannot be played.