How do you do an island select? According to this video tutorial, on blender 2.71 to select just one of two objects that have previously been joined (with control + j), you hover your mouse over the object, and press L. ( Thats a lowercase L )

However, this does not do an island select, but instead pops up a menu, none of which do what is expected. 

How do you do an island select on blender 2.7x?
As you have joined the two objects, they are now one object. In order to edit/select the geometry of an object, you must be in edit mode.

You can press &#8633; Tab to toggle edit mode, or set the mode via the selector in 3D view > header:



Once in edit mode, L works as expected:



Note that you can also select geometry connected the selected geometry with &#9096; CtrlL: