How does the tether (included with the 1030 Plus) work?

It's an elastic tether which is secured to the device at the bottom near the USB port.  Secure enough to save the device in a crash if it disconnects from the mount.  But will break if very severely stretched.

It is interesting that Garmin does not provide instructions for attaching the tether in the User's Guide.

1.  Open the weather cap to reveal the USB port.

2.  On the bottom of the Edge, there is a small opening.  Thread the small end of the tether through that opening.

3.  Once you have a loop visible,  thread the large end of the tether though the small end.  The tether should now be hanging below the Edge.

4.  Close the weather door.

5.  Pass the tether's large loop over your right handlebar, past the brake lever, and up to the stem.

6.  If you are using the out front mount, pass the Edge under the mount to take up slack in the tether, then install your Edge onto the mount.  (If you use the handlebar mount, you'll have slack in the tether to deal with.

I have never had my Edge come out of the quarter turn mount, but I have heard of the mounts breaking, causing the Edge to fall off.  The tether will keep it from flying away. 

(I did have an old style mount for the Edge 705 fail, and that model didn't have a tether.  Luckily, the Edge wasn't badly damaged, and I could just turn around and pick it up.)

I was able to get it figured out after the hobie123 reply. But I agree - Garmin should have provided instructions.

Overall this device has the most confusing instructions ever. Probably because the software people designed a very unfriendly system for the user. Nothing seems particularly intuitive. I loved my Garmin 800 and always thought it was easy to navigate. 

If I could only get a Garmin 800 with a Garmin 1030 Plus screen! Hint hint!!!!

You brought back bad memories of my 705 and that mount that you could sometimes fail to click into. I was riding on the C&O towpath trail and had gone maybe a mile after inserting it one day before I looked down and discovered that it was gone! Backtracked a couple of times but never found it (lots of tall grass and weeds to hide in). So I lost my record of my previous days on the 6-day trip :-(. FWIW I reran the trip 4 years later with my Edge 1000 and the new-style mount.

I'm having great difficulty with the 1030+. This morning, for example my map was disabled and it wasn't intuitive to turn it back on. I finally looked it up at the coffee stop and got it back on. And the route I was trying to ride wasn't working so well either. Maybe the next update will help??? 

Firmware V3.0 has just been release...

I saw that but when I connect online there I don't get an option to update. Is there a way to do this "manually"?

I've never had a Garmin come out of the holder and I do 10,000 miles per year. Until last week my 1030 just flew off after hitting a bump, smashed into 2 pieces. Had to buy a new one. So thank you for tether instructions.

My rides start with a downhill on a poorly maintained street.  Last week, I made a right turn at the bottom of the hill, looked down, and - hey, where is my Edge?  I thought I'd forgotten to put it on the bike.  Then I noticed it hanging by the tether.

I'm glad I started using the tether a couple of generations ago with the Edge 1000.