Identifying modes as they are written on the staff will solidify your understanding of them. Let's first examine some examples with the root note of C.
This is C Ionian (the C major scale).
Ionian contains the scale tones 1 2 3 4 5 6 7. Since the key of C Major has no sharps or flats, no accidentals are present.
This is C Dorian.
Dorian contains the scale tones 1 2 b3 4 5 6 b7. We can see on the staff that our 3rd and 7th notes are lowered with a flat sign.
It's important to understand that the Dorian mode is the same as the natural minor scale except for it has a natural (not lowered) 6th note.
C Dorian is the second mode in the key of Bb Major.
This is C Phrygian.
Phrygian contains the scale tones 1 b2 b3 4 5 b6 b7. We can see on the staff that the 2nd, 3rd, 6th, and 7th notes are lowered with a flat sign.
The Phrygian mode is the same as the natural minor scale except for it adds a lowered 2nd note.
C Phrygian is the third mode in the key of Ab Major.
This is C Lydian.
Lydian contains the scale tones 1 2 3 #4 5 6 7. We can see on the staff that the 4th note is raised with a sharp sign.
It is important to understand that the Lydian mode is the same as the major scale except for it has a raised (sharp) 4th note. C major has an F while C Lydian has an F#.
C Lydian is the second mode in the key of G Major.
This is C Mixolydian.
Mixolydian contains the scale tones 1 2 3 4 5 6 b7. We can see on the staff that the 7th note is lowered with a flat sign.
The Mixolydian mode is the same as the major scale except for it has a lowered (flat) 7th note. C major has a B while C Mixolydian has a Bb.
C Mixolydian is the fifth mode in the key of F Major.
This is C Aeolian. (The C natural minor scale)
Aeolian contains the scale tones 1 2 b3 4 5 b6 b7. We can see on the staff that the 3rd, 6th, and 7th notes are lowered with a flat sign.
C Aeolian is the sixth mode in the key of Eb Major.
This is C Locrian.
Locrian contains the scale tones 1 b2 b3 4 b5 b6 b7. We can see on the staff that the 2nd, 3rd, 5th, 6th, and 7th notes are lowered with a flat sign.
The Locrian mode is the same as the Phrygian mode except for it adds a lowered 5th note.
C Locrian is the seventh mode in the key of Db Major.