I'm glad you like it; what exactly is your trouble with the controls?
Each button on the GameBoy is mapped to a certain note on the F major scale.
If you hold the A or B button (which plays the notes of a high "F" and an "A" respectively), you can also hold down the UP or DOWN arrows on the d-pad at the same time in order to raise or lower said notes by a half step.
You can then use these notes to reproduce the birds songs that you hear repeated in the forest.
A familiarity with music certainly helps here, but even without that, spending a bit of time messing around and listening closely to the background sounds should help!
Edit: For playing in-browser, the arrow keys and "Z" & "X" are used as the GameBoy's d-pad and "A" & "B" buttons.