As mentioned above, a D9 is a D dominant seventh chord with the "ninth" interval of the scale (which happens to be the same as the second, if we're using tempered tuning) added, so it's D F# A C E.

Altered chords are most often (but not always) dominant seventh chords, so the most common notation leaves out the 7 (as it usually leaves out the "dom.").

11th and 13th chords, e.g., D11 and D13 are also dominant seventh chords with the 11th == 4th or the 13th == 6th interval of the scale added _plus_ the ninth, so D11 == D F# A C E G and D13 == D F# A C E B. Please note that the 13th chord does not include the 11th == 4th!

A sixth chord, e.g., D6 or Dm6, however, is not a dominant seventh chord and does not include the seventh. Both contain the major sixth, not the minor sixth, so D6 == D F# A B and Dm6 == D F A B.

The alterations (9th, #9th, b9th, 11th, #11th, 13th) will generally sound better in the upper register, so if they're not playable there, it is sometimes better to leave them out when playing the guitar. Any of them can be replaced by a plain dom. seventh chord, however, one should watch out for chords with alterations that are really other names for the third, fourth or fifth intervals of the given chord. For example, a #11 is the same note as a b5. With 11th chords, one might want to leave out the third, depending on the voicing, especially if one can depend on a bass player filling in the harmony. It's usually best to keep the root in the bass, or alternate it with the fifth, the third, or another interval, in order to keep the harmony clear. Otherwise, the chord will sound like some other chord. Please bear in mind that every chord has twelve names; more, actually, because of flats, sharps, double flats and double sharps. One could continue to triple flats and sharps, but I don't think it really pays.

Having said all that, the ultimate judge is your ears.

The best book on chords I know is Ted Greene's _Chord Chemistry_.