Here's a photo of the A380 flight deck showing the typical sidestick layout.
http://www.airliners.net/open.file?id=957790This wouldn't be much different from a conventional yoke which is designed to be used with either hand.
On dual-controlled aircraft with a side-by-side seating arrangement the captain or PIC usually flies the aircraft from the left seat with his left hand leaving the right hand free for centrally mounted throttles & ancillary controls. On single-seat fighters with fly-by-wire controls the sidestick is usually on the right.
PS. A310 cockpit.
http://www.airliners.net/open.file/1076024/M/