Em/D# is D#, E, G and B. The shape this page opens on is written xx1000, lowest string first.
Note by note. D# is the root, E is the flat ninth, G is the major third and B is the sharp fifth.

Also written Em over D# or Em with D# in the bass. The same chord either way; which spelling you meet depends on who wrote the chart.
There are 3 common shapes for Em/D# on the guitar.
One note away. Change a single note of Em/D# and you have Em (with one note taken away), Emaj7 (with one note moved), Em6 (with one note moved), Em7 (with one note moved), EmMaj7b5 (with one note moved) or EmMaj9 (with one note added).
The common shapes, written lowest string first: xx1000, x6545x, x6998x.
Under the hand. 1 of the 3 shapes here sits in open position, and the first uses 3 open strings with 2 left unplayed. None of them needs a barre. Together they cover the neck from the 1st fret to the 9th.
What kind of chord this is. Em/D# is a slash chord — a triad over a named bass note. slash chords on every root, and what they are for.
The common shapes and the derived voicings come from different places, and both are explained in where the chords and the theory come from.
Shows each chord the way this style would voice it, and marks which of its alternatives belong to the idiom.