Although Greene's patent was the first bolt-action arm kind of, sort of, "adopted" by the US, the design is basically the same as Nicholas Dryse's 1838 and adopted by the Prussians in 1841.
Its major difference(s) from Dreyse's was that the Greene was worked/operated by pushing a release button on the tang, which allowed the bolt to be pulled up and to the rear to expose the chamber for the cartridge.
Two bullets at once were used in an unique arrangement.
A Minie type bullet was loaded, and the bolt was pushed forward passsed its normal position, where a rod seated the bullet forward in the chamber. The bolt was then drawn rearward again where the unique Greene combustible cartridge (with the bullet in the rear of the charge) was inserted into the receiver. The bolt was then pushed forward again, this time down and to the right to close the breech.
To fire, a percussion cap was placed on a cone beneath the receiver, a "ring hammer" (forward of the trigger guard bow) cocked with the index finger, and then the regular trigger squeezed.
That caused the gun powder in the reat to fire the forward seated bullet, with a bullet at the rear acting as a gas check. The powder in the next round, once inserted, then fired that bullet, it leaving its rearward bullet behind. And so on.