Slider crank mechanism converts oscilation of orange conrod to reciprocating translation of pink piston. Hand force is applied to the conrod.

Disk valves open and close automatically due to fluid pressure alteration in the space under the piston. When the piston moves up, the lower valve opens, the upper valve closes. The outside liquid is sucked into the space below the piston. The liquid above the piston is pushed up and flows outside. When piston moves down, the lower valve closes, the upper valve opens. The liquid is pressed from the space below the piston into the space above the piston.

For more about valve action see:

Pump Jack Valves Animation