When I am composing or improvising, I'm thinking of one of two ways (or both) when considering "dissonance": 1) the actual physiological basis of dissonance which has to do with the perception of how the waves of different sounds interfere and are ultimately perceived... an example is when you have two tone sources at the same frequency and one moves gradually to a higher or lower frequency; as they are close, but "out of tune" with each other you can hear a "beating" sound come into place that quickens with increasing distance of frequencies. This changing of interfering waves continues through the point of a single out of tune note becoming an interval between two different notes. Hard dissonances like minor seconds are considered hard because of these frequency relationships. That's probably as good as a definition as I can get there without brushing up on the subject. 2) dissonance as part of a harmonic progression where harmonic structures of relatively greater dissonance resolve to harmonic structures of lesser dissonance. This is in part how we get "V7" chords most favorably resolving to "I" chords, though optionally resolving to "VI", for example.
Now the dominant chords are perfectly acceptable and anyone listening to blues, for example, won't hear the dissonant tritone as "objectionable" even when they're never resolved. As for your link, I've written much music using tone clusters (couldn't tell why you referenced it actually) and the kind of tone cluster I'd use depends on the kind of relative dissonance I want and for what purpose. I might start using diatonic sequences of notes (the "white keys" for example) to get a moderately dissonant start, build tension by moving to increasing chromatic (white and black keys, more dissonant) clusters, and then finally release that by going back to diatonic, but perhaps open clusters... if not some triadic constructs. Managing relative dissonance is done using common practice harmony, too, just not with clusters. I think there's an argument that that's what the practice of harmony is really about.