(wikimedia.org) Part of a Boeing 747-400's autopilot control panel.
Maximum rate climbs and descents are achieved by using a speed climb/descent mode, where the pitch (nose up/down) controls a selected speed. The button FLCH (flight level change) activates such mode (shown above). Each manufacturer has its own name for it, but it's the same functionality. On an Airbus it is activated by pulling the altitude selector knob (Airbus calls it open climb/descent).
In level change climb, the thrust levers are engaged at the maximum thrust for a climb, the autopilot then controls the plane's nose to hold the selected speed. For maximum climb rate, a low speed (ideally Vy) achieves that, i.e., all of the climb thrust minus what's needed for the low speed is used for climbing.
For descents, the reverse is true -- fastest forward speed possible and idle thrust -- combined with the speed brakes. The plane will nose-down to achieve that speed. The rate of descent will be very steep initially, then it will ease off to hold the speed. Speed brakes add drag, so to achieve the same speed the aircraft will nose down more, resulting in a faster descent rate.
As the plane descends into the thicker atmosphere, the descent rate will again start to decrease -- as the plane will be producing more lift and drag. So we can't pinpoint an exact value, but 6,000-7,000 feet per minute is not uncommon.
Once a rate of descent is achieved, whether it's 1,000 fpm or 8,000 fpm, the g-force on the passengers will be 1 g, as there will be no acceleration in the vertical.
(YouTube) A Boeing 777 flight crew demonstrating such procedure.
- A lower altitude is selected
- FLCH is pressed
- The thrust levers are idled -- by hand is quicker than the auto flight system (this does not disconnect the auto thrust)
- The speed brakes lever is deployed
- A faster speed is selected -- the maximum allowable indicated airspeed increases as the plane descends into the warmer air where the local speed of sound is faster (thereby allowing a faster true airspeed, up to a limit).
The above applies for a rapid decompression, other scenarios would likely require a descent, but not that steeply.