Take your triggers out of the stock, turn them upside down and look at them. There is a small screw between the front and rear trigger, and another one behind the rear trigger. They are both adjustment screws, more about those in a minute...
By simply pulling the front trigger the gun can be fired, with a fairly normal trigger pull, without "setting" the triggers. When hunting you'd not likely want to have the set triggers engaged due to the hair trigger nature of them. The REAR trigger is the set trigger and setting it turns the front trigger into a "hair" trigger. On your CVA you must pull the hammer back to half cock to set the triggers - but you can set them by themselves when they are out of the stock. Once set, and the hammer to full cock, the lightest touch on the front trigger should fire the rifle. This is what happens: the trigger is pulled, up flies the rear trigger bar which impacts the sear bar (that thing sticking out at 90 degrees on the lower rear inside of the lock. That spring loaded trigger bar hitting the sear bar causes the lock to release the hammer.
...back to those screws mentioned earlier; The screw behind the rear trigger adjusts the large spring tension located on the upper rear of the trigger plate, housing. That larger spring is the "engine" for the set triggers. The middle screw, the one between the triggers, adjusts how crisp and light your trigger release will be - it sometimes takes a bit of fiddling with to have it working as it should - note that when setting that rear trigger you should hear a click and feel it firmly set - if not then adjustments will have to be made.
That is basically how the whole shebang works. trigger pulled, spring loaded trigger bar jumps up and impacts the sear bar, lock fires.
Several things can cause problems, but for now... out of the gun - can you "set" the triggers by pulling the rear trigger? Can you then "fire" the set triggers by pulling the front trigger? If not, some adjust might get them working.
Unscrew that middle screw a full turn and a half, and try the triggers. Let's hope this is simple.
dave