The Pederson Device (named after its designer) was a (somewhat) modular attachment for the British Enfield and American Springfield 1903 rifles. It consisted of a special device that would be installed into the bolt and receiver of the rifle, allowing it to fire small (but very high power for their size) cartridges in sequence without having to operate the bolt between shots. A semi-automatic conversion kit. These devices were developed in the utmost secrecy, and were referred to as a "Springfield .30 caliber M1918 pistol". Of course, it had been less than a decade since the US had adopted the M1911 .45 semi-automatic handgun to replace their old service revolver. Since the 1911 (which is still used in the US military today) was designed by John Browning himself, and the Central Powers were aware of this, I question the effectiveness of the Pederson's mock designation.
Ideally, the Pederson device could be used to great effect in clearing trenches and laying down fire on the move, two things made difficult by the need to operate a bolt after every shot on normal rifles. The specialty rounds designed for it were not as powerful as the ones normally loaded into their parent firearm, but still maintained effectiveness at just over the anticipated engagement distances.
Using the device was as simple as using the rifle it was meant to go in. The operator needed to remove the standard bolt (something they'd learn in the first few minutes of weapon training, more or less), then slide the Pederson device in place. From there, they could fire from the 40 (!) round magazine as needed.
As of the time of me writing this, I am not entirely sure what the specifics of magazine removal and jam clearing were. Apparently, though, the magazines could be removed and replaced with one hand, so I assume they used a simple latch or spring that could be undone by pulling at the right angle. I don't even have a guess as to how/if you needed to chamber a new round or otherwise operate the bolt to clear a jam.
While the springfield Pederson devices have been common amongst private collectors since the end of the war, the other variants are far more uncommon, and information about them was scarce until very recently. I do know of a collector near to me that has the only non-replica British Enfield variant Pederson device known to still exist. Perhaps it's time I paid them a visit.