Let's look at the normal rhyme:
TONE. TONE. SEMITONE. TONE. TONE. TONE. SEMITONE.
Now let's assign numbers to each step of the rhyme:
TONE(1). TONE(2). SEMITONE(3). TONE(4). TONE(5). TONE(6). SEMITONE(7).
Modes are just scales that start on different parts of this rhyme. For example, the Aeolian mode, famously known as the minor key, starts on 6:
TONE. SEMITONE. TONE. TONE. SEMITONE. TONE. TONE.
There are many complicated ways to work out every single mode, so eventually, a group of clever people came up with this formula to easily find out each mode and gave them each a name. Remember these off by heart and you'll be fine:
Ionian: The Ionian mode is just your regular major.
Lydian: Note number four of the major scale is raised by a semitone.
Mixolydian: Note number seven of the major scale is lowered by a semitone.
Aeolian: The Aeolian mode is just your regular major.
Dorian: Note number six of the minor scale is raised by a semitone.
Locrian: The second and the fifth are lowered by a semitone.
Phrygian: Note number two of the minor scale lowered by a semitone.
EXAMPLE:
C Ionian: C D E F G A B C
C Lydian: C D E F# G A B C
Activity: Work out each scale. The first one is done for you.
1) C Mixolydian: C D E F G A Bb C
2) E Phrygian: ____________________
3) F# Aeolian: ____________________
4) A Dorian: _____________________
5) B Locrian: _____________________
6) D Ionian: ______________________
7) Ab Lydian: _____________________
8) C# Dorian: _____________________
9) G# Mixolydian: _________________
Now try these ones:
1) C D E F# G A B C: C Lydian.
2) E F# G A B C# D E: ____________________
3) F Gb Ab Bb C Db Eb F: _________________
4) A Bb C D E F G A: _____________________
5) Db Eb F Gb Ab Bb Cb Db: _______________