As to the generating, (and the expectation of having to create something "original"): Keith Johnstone writes in Impro:
"The improviser has to realize that the more obvious he is, the more original he appears. I constantly point out how much the audience like someone who is direct, and how they always laugh with pleasure at a really 'obvious' idea. Ordinary people asked to improvise will search for some 'original' idea because they want to be thought clever...The mind can immediately generate a response for what something (imaginary) is - it is more one's desire to appear imaginative (or the fear that an immediate, subconscious response will negatively reflect on oneself) that slows its expression. Our imagination, then, (*without prompting*) is a near-infinite generator of what something could be. Johnstone again:
'What's for supper?' a bad improviser will desperately try to think up something original...he'll finally drag up some idea like 'fried mermaid.' If he'd just said 'fish' the audience would have been delighted. No two people are exactly alike, and the more obvious an improviser is, the more himself he appears."
"...I explain that I'm not interested in what they did, but how their minds worked. I say that either they can put their hand out, and see what it closes on; or else they can think first, deciding what they'll pick up, and then do the mime [of the object]. If they're worried about failing, then they'll have to think first; if they're being playful, then they can allow their hand to make its own decision."Johnstone goes on to show this at work - having a student repeatedly take something from an imaginary box, continually changing the context so they can't plan what (potentially 'clever thing') to take next. J-stones:
"If I make people produce object after object, then very likely they'll stop bothering to think first, and just swing along being mildly interested in what their hands select. Here's a sequence that was filmed...I said:Note this student is not planning these things, but they are being supplied instinctually. I've done this same exercise as a director and the results are the same - eventually the mind supplies its own items without them being consciously planned or strictly supervised.
Keith: 'Put your hand into an imaginary box. What do you take out?'
'A cricket ball.'
'Take something else out.'
'Another cricket ball.'
'Unscrew it. What's inside?'
'What's written on it?'
'Put both hands in. What have you got?'
'What's written on it?'
'Open it and take something out.'
'A pair of rubber corsets.'
'Put your hands in the far corners of the box. What have you got?'
'Leave them. Take out a handful of something.'
'Feel about in it.'
'Taste it.' What's it taste of?'
Take something off a shelf.'
'Reach for something behind you.'
'What is it?'
Notice that I'm helping him to fantasise by continually changing the 'set' (i.e. the category) of the questions."
If that's the Generating, then where does its counterpart Justifying come in?
We'll call this instinct The Justifier, which responds to the question "why" of "why do i have this thing/how do i justify it's presence?" This is instinctual in a scene because it's the same one we use in everyday life to situate ourselves.
This Justifying instinct can be nearly as responsive and usable as the generating, particularly following Johnstone's creed of "Be Obvious! Don't try to be clever" -
If you were in a scene, attempting to justify why you're holding the doggie bag that, say, your scene partner just said you'd brought home, The "Obvious" is: one has a doggie bag from just coming back from a restaurant. No clever "an alien from Saturn's Rings gave me this doggie bag, its got soup recipes in it.
'The obvious' also serves as a much stabler, stronger platform to build the scene on. Doggie Bag's presence could lead to revelation of him having eaten with someone, which could cause tension upon returning home, which could lead to something all the more dramatic. An interesting scene has been created with minimal stress or 'i have to be clever!' pressure on the part of the performers.
That is all that is needed to improvise - generating, and justifying. To build the story and progression, reincorporation is important - as well as other things that can be done to make a better, more interesting scene - including Johnstone's concept of Status, mentioned in this previous post, accepting ideas, etc. - but the above creates the base of all the rest. The fact that improvising is simply what our brain does on its own, means that anyone can improvise. It's not about your funniness, cleverness, or brainpower - all it takes is awareness and using what you have already.
The Justifier is, I believe, our innate pattern-searching and pattern-recognition mental instincts. "Why would i have this?" is searching for a pattern, and Johnstone's 'Be Obvious' injunction reminds one to be comfortable picking the obvious pattern.