There is no adequate manner to depict a birl diagrammatically.  Every teacher has their own way to describe this embellishment.  There are two birls in common use - a heavy birl and a light birl, and it is important to be competent at both.

 In short,  there are two actions in a birl.  The heavy birl is best described as  “Tap and Across”.  This means tap your little finger down on Low ‘G’ and then pull it across the hole thus giving two strikes. Only move you little finger, and try your best to avoid any extra movements from other fingers (this maybe difficult).  Try to feel in your arm that you are controlling your little finger with two different muscles.

 The light birl can be described as an upside down seven on the chanter - slide your little finger down across the hole and back up diagonally. 

A birl can be preceded by a High ‘G’ gracenote or not - the music will tell you this.  Make both Low ‘A’s the same length.  This movement requires to be very fast.

 There is quite considerable variation in the execution of birls.  If your teacher deviates from anything described above this does not automatically mean that something is wrong.  These Birls are however used and recognised world-wide, whereas other styles may not be (yet?).