It is a somewhat dangerous situation IMO, and has been criticised by many in the industry.
Regarding how they work, IIRC when both sticks are used at the same time, the algebraic sum of the movements is used. So if one pilot pulls it fully back, and one pushes it fully forward, they cancel out and nothing happens. There is obviously some complex maths used to determine where the plane goes when receiving two different inputs.
There is also a priority button, which when pressed gives that pilot priority and stops the other stick from working... unless the other pilot also presses for priority in which case the last person to press has priority (I think). There is some kind of warning alarm which sounds saying "Priority Right/Left" when someone presses for priority.
EDIT: A lot of people blamed the crash of AF447 on the asynchronous side sticks, but it was just a small contributing factor. Like I said Airbus designed it with alarms to make it clear who actually has priority - the pilots on AF447 failed to notice they both pressed for priority.
Still, that's no excuse to not have the sidesticks synchronised. To this day I still cannot figure out why Airbus would design them like that.