Ooops, Cynergy's don't have hinge pins. I had a little difficulty with it at first too. Grasp the barrels in the left hand (if right handed), with the vent rib under your knuckles. Grasp the action around the neck of the stock just behind the trigger guard. Place the arc of the receiver against the arc in the barrel block and slide the action upward while moving the barrels in the opposite direction. There will be some resistance as you compress the springs.
Hoppes is a cleaner and does little if anything toward lubrication. I use Mobile 1 synthetic grease available at your local car parts house. You may opt for some of the exotic and correspondingly expensive dedicated products, but I find the Mobile 1 to be quite adequate. It does not have Unicorn's earwax or other exotic ingredients, but it works well.
I wipe the receiver clean of the old grease after each range session, and apply new grease with a disposable flux brush.
I'm right there with Ricklin, RTFM (read that fine manual).