General
If you do not see the Dashboard for Tesla app on your Wear device, first make sure your Wear device is properly connected to your mobile device.
You can do this easily by using other Wear apps that interact with the mobile device, such as receiving a phone call or text message. This will check if there's a more general problem with your mobile and Wear device connectivity.
Wear 1.X
If your Wear device is running Android Wear 1.0, the Dashboard for Tesla Wear app will automatically install when the mobile app is installed and no additional steps are required.
A reboot of the Wear device may help force a resync of apps, but generally this is not needed.
NOTE
There is a potential for lag time up to a few days in the time it takes for Wear apps to automatically install on devices running Wear 1.X.
This is a known issue to Google and can only be resolved by them, until then the only other option is to be patient and give it time for the Wear app to automatically install.
Wear 2.0+
If your Wear device is running Android Wear 2.0, the Dashboard for Tesla Wear app will not automatically install when the mobile app is installed.
This design change is intentional by Google, instead you must install the Wear app yourself from the Play Store app on the Wear device.
You can search for the Dashboard for Tesla app on the Wear device's Play Store, or usually you can open the Play Store app on your Wear device and scroll down to the bottom on the main screen where you'll see a list of companion apps available for install for your device.
Missing / Outdated Versions
Another common problem for the Wear app failing to install or connectivity issues is the official Android Wear app on the mobile device and the Play Services version on either device is not installed or not updated.
You can make sure the official Android Wear app on the mobile device is updated by checking if an update is available on the Android Wear Play Store listing here
You can view the installed Play Services version on your mobile device by finding it with your installed apps in Settings
You can view the installed Play Services version on your Wear device by going to Settings > System > About > Versions
You can update the Play Services app on the Wear device by going to Settings > System > About > Versions and tapping the Play Services menu item
Resync Apps
If you are still unable to install the Dashboard for Tesla app on your Wear device, try resyncing your Wear apps from the official Android Wear app on the mobile device.
As a last resort, remove and re-add your Wear device from the Android Wear app on the mobile device.
For future reference, you can tap the question mark ? button on the top of the Wear screen in the mobile app to quickly return to this post.