Back in June, Blizzard announced that Facebook livestreaming was being incorporated into Battle.net. Today that option has gone live, and it's actually really slick.
Once updated, the Battle.net client will have a little camera icon in the upper-right corner, beside your name. The first time you click it, you'll be asked to log in to your Facebook account and provide all the necessary permissions, after which a pop-out "streaming" window will appear. The window provides simple options and controls for things like the stream title, whether you want your microphone and/or webcam enabled, and who you want to share it with. More advanced settings are available in a separate menu, if you want to tweak things up further.
Once you've got it set up as you like, just click “start stream” (or hit the hotkey) and wham, bam, thank you Zuck, you're on the air. The system is currently in beta so there may be spots of wonkiness here and there, but for the basics of getting up and running, that's the extent of it. I gave it a quick try with Overwatch, and it works really well.
Facebook integration is a pretty big deal, but I suspect that Blizzard is looking to expand Battle.net's streaming capabilities to other places. Battle.net's connection to Facebook can be disabled and enabled in the Streaming section of the advance settings menu, under “Streaming Platforms.” Facebook is currently the only platform listed, but to my eyes it seems pretty obviously laid out to allow for more in the future.