I've updated to Yosemite 10.10.4 but I can't find a way to listen Beats 1 on my Mac...
Apple Music require iTunes 12.2, which is not included in Yosemite 10.10.4 so, soon, Apple should release another update exclusively for iTunes where there should be a button to play Apple Music.
You can get that update from the iTunes menu - select Check for Updates...
If that update isn't rolled out or available, you can listen here:
If you open the Radio tab, click on the plus sign next to 'My Stations' and search for 'Beats 1' it'll be added to your stations and you can stream it. This works with iTunes 12.1.
I'm guessing this only works if you've updated to the latest Music app on iOS, but I haven't tested without upgrading my iPhone.