In addition to physical improvisation, Stanislavsky required mental and emotional exploration of the role. In heavy Method-oriented production of "3 Sisters" (Fall 1999) I asked the actors to do "character's journal" -- you can see it @ 3sis archives.
Improvization as a special discipline is over-rated. It's so organically built within the ACTING that we should see it no more that skill development. There are three main components I ask to choose in Acting One, when we go for Improv Class: situation, character, basic dramatic structure. Simple? Not really.
First, the situation must have urgency and simplicity in order to be established quickly and for all participants at once. Well, we stick with the comedy genre. (We discover right away that we don't know how this "comedy" works -- laws of contrast, comic conflict and ect.)
Second, potentiality. That's why we have to foresee some dramatic development -- expectation of the climax, turning point, resolution. Something ahead, something to aim at.
The Character. Type, Archtype, Stock -- go for physicality. The more grotesque, the better!
For Theatre Theory see THR directory. Also check the Biomechanics!