First change to edge select mode and select the edges.*
Now Extrude, but not the "normal" extrusion (which is called a Extrude Region) you want to Extrude Individual.
You can get to that by clicking the "Extrude Individual" button on the tool shelf, or by pressing AltE > Edges only.
Now, without doing anything press S. It is commonplace to cancel the translation part of the extrusion by pressing Esc or RMB , but that is unnecessary and not needed (kind of like that redundancy).
Here in a glorious full color gif is the super simple process.
* If you use the keyboard shortcut instead of the tool shelf button, the selection mode can be in Vertex or Edge mode.