Although it is possible to change modes within a key along with the chord changes, it is common in Rock, Jazz and Fusion to treat one mode as the basic tonality. A player well known for this is Carlos Santana, who often uses the Dorian mode as the basis for a song.
Shown below is the E form of the C dorian mode. The notes are identical to those found in the D form of Bb Major (Ionian mode). The crucial difference is the positions of the root notes. This is what determines the tonality. Run through the scale ascending and descending, pausing on each root note as you come to it. Notice that the tonality sounds minor rather than major. This is because if you start on C as the root note, the mode contains a flattened 3rd degree.
Once you are comfortable with the sound of the mode, try the following lick which is derived from it.