The chord C/D# that is shown here contains the notes: D#, G, C, E. The root of the chord is C (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 C/D# shown above, place your fingers as follows:
On string number 4, on fret number 1
On string number 3, on fret number 0 (open string)
On string number 2, on fret number 1
On string number 1 (the thinnest), on fret number 0 (open string)
Start strumming from string number 4 (notice not to play strings 5 and 6).