Android Wear can control media playback on your phone, of course, and this doesn't require any setup—it just works. Syncing and playing music on the watch itself is less straightforward. All current Android Wear watches have 4GB of internal storage, and apps don't take up much of it. You might as well get some tunes on there too! Here's how you do it.
After you've got your watch paired with your phone, you'll need to make a quick trip into the Play Music settings to enable Wear syncing. Since you have to use Play Music to sync music with your Android Wear watch anyway, this might be a good excuse to upload your music library to Google if you haven't already. You'll find the setting for Wear syncing toward the bottom of the main settings page.
Any music you keep offline on the phone can be synced over to the watch, so go ahead and find something you want to sync and tap the download button. It can be an album or a custom playlist. Oddly, Play Music instantly starts syncing everything you select for offline caching on the phone over to the watch. Keep that in mind if you only want a subset of your offline music on the watch.
To control what goes on the watch, had back into the settings and open the Manage Wear downloads menu, which is right below the toggle you used to enable Wear syncing. From here, you can see each item that's synced or in the process of syncing. Tap the watch button on the right of each line to toggle sync on and off for each of them. Also note the storage meter at the top that tells you how much more space you have for music on the watch.
You can also open the Play Music app on your watch and choose what to sync based on the list of offline music from the phone. This is a bit clumsier, though.
A few Android Wear watches have speakers inside, but they aren't enabled by the software yet. Even when they are, it's doubtful your music would sound any good coming out of them. That means to listen to music from the watch, you need to pair it with a Bluetooth device. That can be either headphones or a Bluetooth speaker.
For this, you will move over to the watch and open the main system settings and scroll to Bluetooth devices. If your speaker or headphones are in pairing mode, they'll pop up in the list. Just tap and your watch should connect. Note, trying to play music on the watch without a Bluetooth device will result in an error message that routes you to this menu. You can disconnect from an audio device by tapping Unpair devices at the bottom of the Bluetooth menu.
In order to listen to the music you've synced to the watch, open the Play Music app on your wearable. It will ask if you want to play on the phone or watch, and you want to select watch. What you get is a vertically scrollable list of the playlists and albums you've synced over. Tap any of them to listen and tap again to pause.
You can swipe over to the right to access playback controls. These are the same ones that you get when controlling music on the phone. Since this is all self-contained in the watch, you can leave the phone at home and listen on the watch. Be warned, this will drain your watch's battery pretty quickly. At most, you'll get a few hours of playback out of it before a recharge is needed.