A short simple answer could be the same as for any scale: You use the notes of the scale to assemble chords!
This is at least what you do in jazz;
Say, for example, that you have a jazz melody that (for the passage you are harmonizing) uses the notes of a
C mixolydian b9 b13 scale
(C Db E F G Ab Bb). Then you can use chords built on the notes of that scale such as for instance
Bbm9, but you can't harmonize with for instance chords as
Bb△7 since these chords contain notes that are not in the scale that is used in the melody.
But I believe more data is needed from the question. Are the scale notes the only ones allowed or available, or are actually other notes available to use for the chords? -- For example: Harmonizing with only the five notes of a pentatonic scale will give you a very different result than when you use a pentatonic scale in a jazz blues context where you actually have other notes available for harmonizing (and thus the scale, in some sense, is actually not only a pentatonic).