Softshells lack the horny scutes of other turtles. Their carapace is covered in skin over a reduced bony plate, and that skin is thin and well supplied with blood vessels. Oxygen dissolved in the water crosses it into the bloodstream in useful quantities.
A second route runs through the throat. Softshells rhythmically draw water into the pharynx and expel it, moving it over villus-like projections dense with capillaries. The behaviour looks like a slow gulp repeated for minutes on end. Together the two routes let a resting animal remain submerged far longer than lung capacity alone would permit.
The long snout is the complement to this. When conditions call for air, a buried softshell in shallow water can extend the tubular nose to the surface without exposing the body, breathing while staying hidden in the sand.