It seems the current radio function is connected to TuneIn, so that's what I'll use. It should be possible to use other services but I'm still struggling there. In the SqueezeBox client you can enter URLs directly.
A. Using TuneIn.com
1.1 Create a TuneIn account on https://www.tunein.com
1.2 Look for the channels you want and add them to your personal favorites. You can have multiple folders, but I had some troubles with that. Just stick them in the default 'General' folder.
1.3 Rearrange the channels to your liking.
Note: it can take several minutes before any updates in TuneIn show up on the SqueezeBox LMS.
2. SqueezeBox Settings
2.1 Settings / Advanced / TuneIn Radio
2.2 Add the username you used for your TuneIn account
Note: you may have to wait a few minutes before the radio stations from TuneIn show up.
3. SqueezeBox Client
3.1 Radio / My Presets
3.2 Pick the channel you like and it will play
B. Entering URL manually
1. Find the streaming URL (Google for a radio station name plus the keyword 'stream' may help)
2. Launch the SqueezeBox Client
3. Go to Radio / Tune In URL (which has nothing to do with the TuneIn website!)
4. Enter the URL, for example https://stream.arrowcaz.nl/bluesboxonline
5. You may have to hit the play button