The Modes are tools for improvisation. Think of them as a part of your color palette. In jazz, each chord symbol is considered not only to represent a Chord, but also one or more scales upon which to improvise. Thus C maj7 not only represents the chord [C E G B] but also the C major scale (also known as Ionian Mode) as an option.
If we were improvising in the key of C major, and all of the chords were diatonic to (containing only the notes of the C major Scale) then one could simply think "Dm7 = C scale from D - D; G7 = C scale from G - G" etc. and be done with it.
Many modes contain one other factor called the "Avoid Note." This term is a bit unfortunate because it does not mean that you cannot use the "avoid note" but that it needs special handling. (A better term would be the "handle with care note").
In the Ionian mode (The major scale) the "avoid note" is the 4th scale-step or "F". This is the suspended 4th or the 11th (which is not generally used on a Major chord since it creates a tritone between it and the 7th.) When improvising, you want to avoid placing the "F" in a prominent position -- such as ending on it on a long note over a C maj chord (C D E|F-----|). It is o.k. to use in passing, such as (C D E F| G).
The Mixolydian mode (The C scale from G - G) similarly avoids its 4th scale-step (C) since again that is the sus4 or the 11. Now, if the indicated chord were G sus 7 or G 11, the "avoid note" becomes the 3rd or "B" since the sus 4 is now the chord tone.
The Aeolian mode (natural minor) does contain an "avoid tone" -- the 6th scale-step, which represents a b6 or b13, which creates a tritone between the 9 and 13 (or 6).
Not all modes have avoid notes. The Dorian mode does not so no special care is needed.
Minor 7 chords have at least 3 possibilities -- Dorian minor, Phrygian minor, or Aeolian minor (same as Natural minor). The most frequent scale for a minor chord, regardless of the key, is Dorian since it contains no "avoid notes". You are usually safe with that choice. This is because, a minor 7 is most frequently acting as a II of a root movement II - V progression. In the Key of C -- Besides the actual II - V of Dm7 - G7, equivalent II - V movements are Am7 - D(?); and Em7 - A(?) (The D(?) and A(?) could actually be dominant or minor 7) and therefore you would most likely want to use dorian.
Similarly, regardless of the key, for any dominant 7 chord, you would use Mixolydian.
I hope this helps a little. When studying modes, you need to learn the "avoid notes", if any.
