How does this hand pump work
From the disassembled photo, it looks like if you put the parts back together the pump will work for Dunlop valves and Presta/Sclaverand valves (roughly any narrow type valve). You should be able to put the rubber and the red thing the other way around in. Such that the narrow pointy thing of the red part points outwards and the rubber has a wider opening to the outside. That way it should fit car valves.

For the usage, it should work like any other pump with a lever.


(for Presta/Sclaverand valves, screw out the round thing on the top of the valve, to unlock the valve)
With the lever like in the first picture push the pump on the valve. 
Then fold out the lever like on the middle picture. This compresses the rubber such that it squeezes around the valve and makes the connection pump-valve air tight. (With Dunlop, this step sometimes failed for me with Dunlop valves as their top part is a bit on the short side, so compressing the rubber pushes the valve out of the pump. If that happens, try again and push pump and valve together when flipping the lever. Once the lever is flipped, the rubber should keep the valve in place)
Pump air
fold the lever in again
pull the pump off the valve
(screw in the "lock" of the Presta/Sclaverand valve if applicable)