Without a nearby iPhone, the Watch can't answer calls or receive notifications, but you can use Bluetooth headphones to listen to music stored on the device. Here's how to set it up.
Step 1: Put music on your Watch
Of the 8GB of storage on the Watch, up to 2GB can be used for music storage, which roughly translates to about 500 songs. To get music on your Watch, launch the Apple Watch app on your phone, then head to Music.
First, decide how many songs you want to sync with the Playlist Limit option. You can set a limit based on storage capacity or number of songs. When that's set, go back and choose the playlist you want to sync.
Just remember that if the size of the playlist exceeds whatever limit you set, not all songs will make the cut. If you want to avoid this, create a playlist using your Playlist Limit option as a guideline.
Now the hard part: wait. Place your Watch on its charger and kick back as the playlist syncs. In my experience, it's a time-consuming process, so you might want to do this overnight.
Step 2: Connect the Watch to Bluetooth headphones
Since the Watch doesn't have a headphone jack, you'll have to rely on Bluetooth headphones. There are quite a few available these days -- here are some of the best BT headphones (and some of the ).
To connect the Watch to Bluetooth headphones, put your headphones (or speaker) in pairing mode. Then go to the Settings app (on the Watch) > Bluetooth, and your headphones should appear. Select them from the list, and you're set.
Step 3: Choose the source and hit Play
When your music is done syncing and your headphones are connected, you're almost ready to use your Watch like an iPod. The last thing to do is change the music source in the Music app.
On the Watch, go to the Music app. Force touch (tap and push in on the screen) to bring up more options. Select Source > Apple Watch. At this point, the playlist you synced should appear in the app and you're ready to listen to music without your iPhone.