Start by opening an image of a swing. Knockout the background.



Select the upper wood wok of the swing using the polygon lasso tool.



Press Ctrl+Shift+J to cut and paste the selection into a new layer.

Select the puppet sitting on swing. Press Ctrl+Shift+J to cut and paste the selection into a new layer again.



Create several duplicates of this layer. Scale up the duplicates sequentially.



Hide the duplicate layers. Create more duplicates of this layer. This time scale down the duplicates sequentially. Move these layers below all the layers in order in the layer palette.

Open animation window. For the first frame unhide the smallest swing layer as it will appear the farthest.



Duplicate frame. Unhide the next swing layer that should be a little bigger than the previous one.



Keep duplicating frames and unhiding the sequential duplicates from farthest to nearest.



Create more frames and unhiding the sequential duplicates, this time from nearest to farthest creating a reverse sequence.



Press Ctrl+Alt+Shift+S to save an optimized animated GIF.