Hi Alex.

Highland Pipe fingering is a member of a group of Bagpipe fingerings found in western edge of Europe called "Half-closed". This means that the notes of the second (Upper) hand above D (Pipes in A mixolidian) are played with most or all of the Lower hand fingers on the Chanter.
This facilitates the use of loud lower grace notes with out the need to move a lot of fingers simultaneously. It also helps steady the pipe whilst playing.

Below is the fingering Chart for GHB
o= open x= closed
          lower,Upper hand
Bottom   G xxxx xxxx Reed end
         A oxxx xxxx
         B ooxx xxxx
       C# xoox xxxx
         D xooo xxxx
         E oxxx oxxx
       F# oxxx ooxx
         g oxxx ooox
         a oxxx xooo

The trick when learning to play this fingering is to make shore that you don't make "crossing noises" that is short unintentional notes as you go from one not to another. On the full size Pipe these are very distracting and learning not to do them at the beginning will save you a lot of work later on, believe me I know.
A good exercise is to go from every note to every other note, listening for the dreaded crossing noises.
A pattern I use is starting High a play a to G, a to F#, a to E, and so on down to a to G and back. Now repeat substituting High g and all the other notes including going up to notes above the chosen note.
This might seem a bit over the top but it will work and later on when you begin to learn the grace note patterns it is almost unavoidable if you want to be a fluent Piper.

Good luck
PP