Updated Monday, October 28, 2013
It requires Bluetooth 4.0 LE, which is only in a few devices right now (But that number will grow). If your device doesn't support Bluetooth 4.0 LE, you're out of luck. Period. Buy a new phone if you want to use a Galaxy Gear.
The good news is that it's mostly software - the required hardware is becoming standard (but isn't yet). Theoretically, it should work with many Android phones as long as they run Android 4.3+ and support Bluetooth 4.0LE. The bad news is that someone needs to identify and reverse-engineer this software in order to enable the Gear to work with other devices. The other good news is this is happening very quickly! Look below!
A thread on XDA Developers (Many thanks to Oleg, who posted this in his answer and deserves upvotes) has interesting news! The software needed has been identified, and the APK's have been extracted. According to one user (Our hero, Oleg), following the steps on the thread and using the files provided there allows you to pair the watch and unlock it with a Nexus 4. A basic description of the processis follows...
- Install all the Samsung APK's from this upload, provided by XDA User blazespinnaker.
- Install com.sec.android.fotaprovider from the same upload.
- Run Gear Manager. If you have errors, close it and run it again(?).
- Pair Manually with your Galaxy Gear.
Note that this is still not a perfect solution. Some features may not be working. However, you should apparently be able to unlock and enable ADB!
I'll update this answer as more information becomes known.
But for the rest of your question (about ADB).
This article indicates that you can enable ADB mode on the Galaxy Gear itself, which is actually kind of exciting. The steps are simple. The article also has a helpful video!
- Swipe to "Settings"
- Scroll all the way down to "Gear Info"
- Enable "USB Debug"
If you're on Windows, you'll doubtlessly need the Samsung USB Drivers. But other than that, you should be pretty much set!