I just bought one of these:
It was fairly cheap so, unsurprisingly, in "Settings" I don't see any way to select "developer mode".
How can I go about enabling developer mode (USB debugging) to install apps via ADB?
If its an Android Wear watch (and it seems so) there is no options on the watch directly. It depends on the phone it is paired with, and all the options are available on your phone.
I have a Moto360 and I also don't have any developer options on my watch. If you plan to develop for Android Wear, you need to install everything on your phone, which will push all needed resources to your watch.
You should follow the steps mentioned here: Creating and Running a Wearable App.
It's quite similar to the phone : go to Settings -> About, then tap on the Build Number seven times. It will enable the Developer Options where you can enable ADB Debugging.
If you can't connect your watch to your computer via USB, you can always enable the Bluetooth debugging following these steps : Debugging over Bluetooth
Execute these adb commands :
adb forward tcp:4444 localabstract:/adb-hub adb connect localhost:4444
If the second command fails, try replacing localhost with 127.0.0.1 .