You use the "Retouche" brush in Aperture and set it to "clone".
Option-Click on the location you want to clone from to select a source, and then brush over the location where you want to clone to. The cloned region will follow the shape of the brushed area. You do not lasso the shape to to copy and paste it like in Photoshop.
For example: Duplicating a penguin: The sourcepoint has been set to the beak of the second penguin, and then I brushed along the path where I want to penguin clone to appear.
If I brush the whole area eventually the penguin will be copied completely. You'll have to experiment a bit with the brush size and softnees to ensure that the cloned object will blend in.