Dorian is the second mode of the major scale so we get it by starting from the second note instead of the first. In the Key of C major the Dorian mode would be D Dorian, the notes would be D-E-F-G-A-B-C-D. The same notes as C major but starting from D instead of C.
The Dorian mode is normally used over a m7 chord, this is because the II chord in a major key is a m7. See our post on building chords from the major scale for more information. So if we have a chord progression which contains a II chord we can use the Dorian mode to solo or write a melody over it. We can also write chord progressions which resolve to Dorians I chord. For example dm7.