The chord D#/G that is shown here contains the notes: G, A#, D#. The root of the chord is D# (The lowest sound - the bass - is G). The scale from which the chord is derived is Major, and the degrees of the scale are: 1, 3, 5.
To play the chord D#/G shown above, place your fingers as follows:
On string number 6 (the thickest), on fret number 3
On string number 5, on fret number 1
On string number 4, on fret number 1
On string number 3, on fret number 0 (open string)
Start strumming from string number 6 (notice not to play strings 1 and 2).