The valve works in the same way as my Boulton and Watt Bell Crank engine D valve works: The Valve in this case will be "bobbin shaped" with a hole from top to bottom to let the exhaust through. The centre of a bobbin is of a smaller diameter than the two ends...this centre bit is where the inlet pressure is, the two wider diameter ends of the bobbin close off the ports or expose them to the exhaust/inlet as required.
If you want something confusing try the Bodmer's Sliding Cylinder Steam Engine that Anthony Mount did. On that the piston rod is also the valve/steam inlet/exhaust
Jo