I found solfa an invaluable tool for understanding the modes (although you do really need to be familiar with solfa first so what I put next may just fox you entirely if you're not...).
There are three major and three minor modes.
The Ionian is the basic diatonic major (d r mf s l td').
The Lydian is like the Ionian but with a raised 4th (d r m fi s l t d').
The Mixolydian is like the Ionian but with a flattened 7th (d r mf s lta d').
The Aeolian is the basic natural minor (l, t,d r mf s l).
The Dorian is like the Aeolian but with a raised 6th (l, t,d r m fis l).
The Phrygian is like the Aeolian but with a flattened 2nd (l,ta, d r mf s l).
The Locrian is the odd one out because of the diminished 5th and the fact it has two 'altered' notes. It is also very rarely found in musical examples.
Describing them in the above way makes the relationship between the modes very clear and easily transposable (I'm afraid having them described as 'the white note scales' only served to make them as clear as mud to me

).
Of course you can also describe them in the 'authentic solfa' eg r mf s l td' r' for the Dorian mode.
Petrat, I think 'She Moved Through the Fair' is Mixolydian? And 'Eleanor Rigby' is basically major but with a strong Lydian flavour in parts? Forgive me if I'm wrong here.
I

the modes!!!