Google has posted a few videos to YouTube showing how to use the special Bose QuietComfort 35 MK II headphones with embedded Google Assistant features. The features themselves are rather simple and easy to use, so the tutorials are short, but detailed. There are three videos in total, none more than two minutes long, and once you've watched them all, you should face no surprises from your new Assistant-enabled headphones. To put it as simply as possible, everything revolves around the Assistant button on the headphones, and making use of the features boils down to using that button and speaking your commands or replies.
A quick press of the button at any time will give you your notifications. After a notification plays, you'll have an opportunity to reply by voice depending on the type of notification, allowing you to take actions if Assistant is compatible, and send messages back in certain apps. iOS users should be cautioned that they can hear notifications, but cannot take action on them. When fresh notifications come in, you can press the button to hear and possibly reply to them, or simply ignore them. If you continually ignore notifications from a certain app or sender, Assistant will eventually play those notifications at a lower volume.
Actually using Google Assistant works much like it does on your phone. Rather than the home button on your phone, you're holding down the Assistant button on your headphones. Whereas a quick tap will have Assistant read out your notifications, holding the button a hair longer will actually kick Assistant into listening mode, allowing you to issue commands or control your media just as you would with your phone. Commands that would result in pulling up a web search on your phone will usually see Assistant reading an excerpt of the first result to you, allowing you to do quick research without having to pull out your phone. It is worth mentioning that asking Assistant to play some music on YouTube will require unlocking your phone and keeping the screen on, unless you subscribe to YouTube Red. There are other methods of being able to play YouTube without your screen being on, but many of those require rooting your device, which comes with its own difficulties and caveats, or downloading potentially dangerous third-party YouTube clients from outside of the Play Store.