The "idea" behind modes is basically this: imagine a normal major scale, for example C major, which is C D E F G A B C. The scale itself is called Ionian. Then move to the next note and form a scale that starts and ends with it and build it using the notes from the Ionian scale. What you get is D E F G A B C D (D Dorian). Then move the next note from the Ionian scale and do the same, which gets you E F G A B C D E (E Phrygian). Rinse and repeat until you get to B Locrian (B C D E F G A B).
What's useful about this is that if you play in a song in C major which consists of, say, the chords C major, D minor, F major and G major and want to create an interesting bass line, using the modes that start with the same notes as the root root notes of the chords will always lead to good-sounding results. It'll help you avoid "wrong" notes and you'll always know where the root is. For example, when playing over the C major chord use C Ionian, when playing over the D minor chord use D Dorian, and so forth.
This isn't the only way to use them, of course, they also sound cool in other contexts.
So, yeah, DRay521 is right, the "correct" way to play Dorian in E major would be F# Dorian because E Ionian is E F# G# A B C# D# E.