The back does not come off (case is in one piece); it's the bezel -- the metal rim that holds the front glass crystal.
There is a small notch in the rim of the bezel (on mine, this aligned with the 'lower left' lug on the case around 7:00 on the face). Be careful as there is an O-ring to waterproof the watch, and this notch goes right into the groove where that O-ring is located. Use a case knife or similar stiff but fairly thin-edge blade to pop the bezel off (it snaps off). Then gently remove the outer plastic ring, noting carefully how the notches are aligned.
The inner module now can be lifted carefully out - the two 'pushers' will not fall out of the case when you do this. The battery is a 3V lithium CR2025, and you will need a fairly small straight-blade jeweler's or optician's style screwdriver to remove the one screw that holds down the battery bracket - it may be tempting to bend this out of the way to change the battery, but please resist that temptation...
Put the module back in the base, put the ring back over the dial plate, and carefully snap the bezel back in place with its notch aligned as you found it. You might want to check and/or lubricate the O-ring as you do this.
Instructions for initializing the movement are printed inside the case: they list the switch for the 'recessed' button as A, and the pusher as B. In case you didn't note them before closing the case: to reset:
1) push A once. (Display will read "SET"
2) Push A until hands are exactly on 12:00 (and display reads "12"
3) Push B once to start reception
You then follow the standard procedure of putting the watch in a window facing Fort Collins, Colorado, until it picks up the time signal and synchronizes itself.
If you need more assistance with the physical module, there is contact information on it from its manufacturer:[email protected]
Model number on my module is AR600 WWVB (37.5mm)