Airliner speed when descending through 10,000 feet
Note that the speed you saw would have been ground speed not air speed. But in any case, you generally descend with the autopilot in a mode that pitches to hold an airspeed, called "Speed Mode" or something similar.  The other option is to descend in a mode that pitches to a vertical speed, called "VS" mode.  Speed  Mode is used most of the time.  You set the target speed the AP will maintain with a dial on the autopilot panel that moves a bug on the speed tape.

When you start a descent you will usually dial the speed you want to descend at, engage speed mode, then pull the thrust to idle, and over you go. Say you are descending with the bug at 290, which means the bug is set to 290 on the tape and the airplane will nose up or down as required to hold that speed, and in this case you are in some kind of dive. 

As 10000 ft approaches, say passing through 12000, you just dial the bug down the speed tape to 250.  The airplane will pitch up a bit and start decelerating, then start pitching down again to maintain 250.  You try to time it so you are hitting 250 just as you are passing 10000.

ATC doesn't know your indicated airspeed, only your ground speed, so a controller has to estimate your airspeed based on the wind and ground speed.  This means being a few knots over the limit won't get you busted.

If you screw it up and are still too fast by more than say 10-20kt passing 10000 (or maybe because of some other imperative), then you'll dump some speed brakes to slow down faster.  But like I said, 10kts too fast passing 10 is not a big deal.