Don't know if this will work but I found them on the internet..
Instructions
1Hold down the center button which is usually on the right-hand side of the watch for 6 seconds. This activates the "Mode" setting that allows for the time to be set.
2Determine which time zone the atomic watch is set to. If the second hand is at 11:00 it is set to Eastern Standard Time, if 10:00 it is set to Central Standard Time, if 8:00 it is set to Mountain Standard Time and if 7:00 it is set to Western Standard Time.
3Press the top button for each time zone westward you need to pass until you get to your time zone, or press the bottom button once for each time zone eastward you need to pass.
4Press the center button twice.
5Set the watch down for 20 to 30 minutes while it sets itself.
or this this, this is for the wrist watch and I haven't seen a picture of yours if the buttons are the same.
How to Use a Hammacher Schlemmer Atomic Wristwatch
Instructions
1Set the watch near a window in order to manually receive a time signal. Push the button on the bottom right-hand side of the watch and hold for a few seconds. Release the button. Once a signal has been received, the watch will automatically receive time signals at least once a day and should not require manual signal reception under normal conditions.
2Adjust the time zone if necessary by pushing the button on the bottom left-hand side of the watch to change to the time zone mode. Push down and hold the button in the middle right-hand side of the watch until the display begins to flash. Push the button on the top right-hand side of the watch until the desired time zone is displayed and press the button in the middle right-hand side of the watch to return to the timekeeping mode.
3Start the watch's stopwatch by pushing the button on the bottom left-hand side of the watch four times. When the display reads 0:00 press the button on the top right-hand side of the watch to begin timing. Push again to stop timing. Push the button in the middle of the right-hand side of the watch to exit the stopwatch mode.
4Display the alarm time by pushing the button on the bottom left-hand side of the watch. Push and hold the button on the middle of the right-hand side of the watch and hold for a few seconds until the display flashes. Push the button on the top right-hand side of the watch to change the alarm time and press the button on the middle of the right-hand side of the watch to exit the alarm mode.
5Use the watch backlight in poor lighting by pushing the button on the top left-hand side of the watch and holding down. Release the button to turn off the light.
Wish you luck. Hopefully someone out there will have one and give more precise instructions. Otherwise you will have to use these as a guide and just try combination of button.