You can have your butcher butterfly a chicken (or a game hen or a quail), but it's fairly easy if you want to give it a try. It's easiest when the chicken is cold, patted dry of any moisture.
Turn the bird over, so that the backbone is facing up, breast side on the counter. Using sharp kitchen shears or a chef's knife, cut down, along one side the backbone. Repeat on the other side to remove the backbone. (Reserve the bones for stock.)
Open the bird as much as you can. Lay a clean kitchen towel over the open cavity. Place the palms of both hands on top of each side of the breastbone, and push down to flatten the bird as much as possible.