The letter names the key (and major scale), and the mode determines which note the scale starts on. In the case of mixolydian mode, the scale starts on the 5th note.
So "E mixolydian" implies that you have an E major scale (E, F#, G#, A, B, C#, D#) that starts on the 5th note of the scale: B.
Therefore, the E mixolydian scale would look like this: B, C#, D#, E, F#, G# A. Still the key of E, but it starts and ends on B instead of E.
Here's a link to a page that's pretty good at showing the scales of the different modes: http://musictheoryfundamentals.com/MusicTheory/modes.php
All of the modes are in the key of C, so you'll note that the key signature is the same: no sharps or flats in any of the scales. The only thing that changes is the mode, which simply means the starting and ending note. Same C major scale, you're just starting on a different note with each mode.