How to interface to LPG consumption meter
Start with earthing the red (!?) wire to the ground of the arduino.
Apply 5 volts via a 10k resistor to one of the black wires and also connect the black wire to the arduino as well.
Basically :

5V ----(10K resistor)---+---Black wire----( Gas Meter)-----ground
                        |                              
                        |                             
                        +--- arduino digital input


You should either get a high or a low signal. Try the other black wire, it might be inverted (as in high and then pulse low, vs low and then pulse high).

Failing that, pop the top off that cover and have a poke around. Might give you a clue as to what's what.