A common tuning variation when playing in the key of D is to tune the low E string down a tone to D and leave the other strings in standard tuning. This is often referred to as dropped D tuning. The low D note is written on the fourth leger line below the staff. In the TAB it becomes the open 6th string (^ = D).
Take care with the slurs in this piece. Practice the melody by itself until you can play it smoothly all the way through. Use your metronome and count out loud until you get it right. It is also worth practicing the right hand separately.