Modes are taught two ways, both have been mentioned here. Relative as you mentioned and Parallel as the other posts covered. The Parallel method is much easier to use, the Relative is much easier to teach. Now that you know how to make them, how to use them becomes important.
Chris touched on a very important point.
"But the general classic idea of modes is to play a piece of music in one mode entirely, using the root note of the mode as tonic for the entire piece."
1, 2, 3, 4, 5, 6, 7, Major scale which is Ionian.
1, 2, 3, #4, 5, 6, 7 Lydian
1, 2, 3, 4, 5, 6, b7 Mixolydian
OK that's the major modes - want a day dreamy major mood take the major scale and sharp the 4th. Want the Mexican sound or the Blues sound (mood) take the major scale and flat the 7th. Want an up beat attractive mood use the major scale.
The minor modes revolve around the natural minor scale which is Aeolian. Want Dorian sharp the 6th back to a natural 6. Want Phrygian flat the 2. Locrian has both a flatted 2 and 5. Want a basic minor (some say sad) mood then just use the natural minor scale.
Only reason IMHO to bring in a mode is for it's mood. How often does a song change moods - certainly not over every chord change.
To gather this mood you have to select the chords that will sustain the mood you want. A chord progression will normally call attention to it's tonic - which may not have anything to do with the mood you want. A modal vamp will stick around long enough to let the modal mood develop.
I found Parallel with a modal vamp would do what I wanted. After I found that I never went back to Relative.
http://tamingthesaxophone.com/jazz-modes.html For Parallel.
http://www.riddleworks.com/modalharm3.html Modal vamps.
My 2 cents on the subject.