1967 340. Bought a new pair of Gaz shocks. Problem is I don't know how to extend them? What's the secret to extending them and then contracting like one would do with the shocks I'm familiar with?

 

All shocks basically work the same way. Fluid is restricted by valves which controls the rate by which the shocks open and close. From the photo your GAZ shock has an adjuster. Brute force ie pulling the two ends so the shock expands is the only way to extend its length but by turning the valve from one extreme to the other will make it easier or harder to extend it as this adjuster opens or closes the valve.
On my Lotus Seven which had adjustable Spax shocks they had a rose joint each end which allowed me to put a screw driver in each hole and use them as "T" bars to pull the shocks open. I stood on the screw driver in one end with both feet and pulled the other end like I was withdrawing Excalibur from the stone.

 

I hope that's the answer. On any other shock I've encountered I could grab it and pull it out. These not so much. I'll get a bit rougher with it.

 

Could you turn the stiffness down?

 

All the way down.

 

Firstly. Are they the right range of motion shocks for the car?
Secondly if they are, you are going to have to pull harder & make sure that the setting is all the way down & not all the way up.