READING A GMT WATCH
This is the diagram we're going to use. The minutes hand, the 12 hour hand, the 24 hour hand and the date window are represented.
(The second hand has been left out to keep the dial less busy)

Like on a conventional watch, the 12 hour hand rotates twice a day, displaying AM and PM time on the dial.
On a conventional watch, the hand would be showing 10:10. But one would not be able to tell if it were AM or PM time

The 24 hour hand rotates just once a day, pointing at the outer ring, or bezel. And by doing so, it helps to differentiate between AM and PM time.
Here, the 24 hand points at 10:10 (10:10 AM), and not 22:10 (10:10 PM)

Reading the display might turn out to be quite tricky at the beginning, yet once one gets the hold of it, it becomes a child's play:
As one can see, the 24 hour hand completes a single revolution, whilst the 12 hour hand rotates twice, successively displaying AM and PM time.
SETTING A GMT WATCH
Here lies the particularity of the independent 12 hour complication first used by Rolex, and now Blancpain, Omega and Seiko:
Pulled in setting position 1, the crown makes the 12 hour hand jump forward or backward without affecting the rest of the mechanism.
When crossing a time zone, the wearer can simply adjust the 12 hour hand to local time, whilst the 24 hour retains home time.
The date indication is also for local time, so it only changes when the 12 hour hand has completed two revolutions

Pulled in setting position 2, the crown moves the whole 3 hands forward or backward and hacks the second (except on the Blancpain, where the second doesn't hack)
Using a GMT watch like a professional 
It has been brought to my attention that aviation professionals and licenced amateur radio hobbyists use their 24 hour hand to display UTC time, or Zulu Time:
They set the whole watch on Greenwich Mean Time (GMT 0), and then set the independent 12 hour hand on local time
In our example, if it is 10:10 AM in New York (GMT -5), the whole watch must be set 5 hours forward to display the Greenwich Mean Time (GMT 0)
The independent 12 hour hand can then be set 5 increments backwards to display local New York time (GMT -5)
After this operation, the independent 12 hour hand is no longer synchronized with the 24 hour hand, unless it is being set 5 increments forward
Using a third timezone 
It is possible to use a rotating bezel with 24 hour subdivisions to indicate a third time zone:
Simply rotate the bezel by one increment, per hour of time zone.
- Rotate the bezel counter clockwise if the third time zone is Eastern to home time
- Rotate the bezel clockwise if the third time zone is Western to home time
Example: if home time is New York (GMT -5), and third time Paris (GMT+1), move it 6 increments counter clockwise (+6)
If home time is New York (GMT -5), and third time San Francisco (GMT-, move it 3 increments clockwise (-3)
Using the GMT display as a rough solar compass 
This tip also applies to practically all the other watches equipped with a 24 hour hand. The wearer can use a 24h dial for approximate navigation anywhere between the Tropic of Cancer and the Arctic Polar Circle:
Important! Both the 12 and the 24 hour hand must be synchronized to display local time
Method 1: laid horizontally, the dial will head North if the 24 hour hand is pointed towards the sun
Method 2: if the 12 hour hand is pointed at the sun, the 24 hour hand will point North
The margin of error directly depends on the difference between local official time and actual local solar time. But one doesn't need to get too much in the technical details for approximate urban navig