The chord G#/D# that is shown here contains the notes: A#, G#, C. The root of the chord is G# (The lowest sound - the bass - is D#). The scale from which the chord is derived is Major, and the degrees of the scale are: 1, 3, 5.
To play the chord G#/D# shown above, place your fingers as follows:
On string number 3, on fret number 3 with finger number 1 (index finger)
On string number 2, on fret number 4 with finger number 3 (ring finger)
On string number 1 (the thinnest), on fret number 3 with finger number 2 (middle finger)
Start strumming from string number 3 (notice not to play string 4).