The sidesticks are two completely independent controls. They send an electrical signal based on the position they are in, and they add both the inputs together (up to the equivalent of full-deflection). So if both pilots make half-left inputs, the computer says that's full-left. If one puts full forward and the other puts full back, computer says thats neutral. If you did that, you'd get a "DUAL INPUT" aural warning. You should never hear that.
You NEVER use both side sticks at the same time.
(The exception to this is if one pilot takes control from the other pilot AND presses the red takeover button AND verbally takes control. You would then get a "PRIORITY RIGHT/LEFT" aural alert. You would always use the takeover button because you just do not know what control input they are making).
Example, you have a fairly inexperienced F/O landing the aircraft, who has passed his line check and is flying with an "ordinary" captain. The captain realises at 20ft the F/O hasn't started the flare. If the Capt pulled back on his sidestick without pressing the takeover button, and then the F/O pulled back on his sidestick a split second later too, both inputs are counted and added together (half backstick + half backstick = full backstick demand). Since you don't know what the other person is doing, you must take full control using the takeover button, or leave them in control. You can't just "help" them on the controls because that will often be worse than not intervening at all.
The only controls that are linked together are the rudder pedals. If one pilot's rudder pedals moves, so does the other.