Although the basic premise of improvised storytelling is to keep it simple and logical, there's actually a bit more to it than that. There are definitely other skills to use to make your story really be effective.
One important skill is having a sense of where you are in a story. This is almost essential for making those choices when the next step can be one of several things, any of which lead down wildly different paths. It can also help see how particular events can be used to show the progression of the character.
Quite often in a story, certain things will happen several times. Their outcome or impact on the story or character differs depending on where you are in that story.
For example, say a particular story is about a guy who hangs around a bowling alley. Almost certainly this guy is going to bowl a couple of times. Probably much of the time the bowling will be background / environment work in that it won’t be significant. The bowls themselves won't be important, but might be used to show mood. I'm a great believer that saying "I'm angry" is (generally) much less interesting and realistic than doing what you're doing in an angry way.
In our story, for example, 2 people could have a heated discussion whilst bowling and we can see how the rollercoaster of emotions affects their bowling. We can see what they're feeling without it having to be explained to us. A sadly bowled ball is vastly different to a triumphantly bowled ball.
But, occasionally, some actions will be given a high prominence in the story.
At the start, a bowl could help define the character (or establish the ordinary world) of the hero. Put simply: If he scores a strike, he’s a great player; if he scores a gutter ball, he’s an awful player; and a middling score means he’s an average Joe.
Depending on where he starts, you can often predict what later bowls will be like. To show what I mean, let's look at a classic “comeback” story:
The hero starts the piece bowling extremely well – he's at the top of his game. But something happens and he starts playing really badly. This is a turning point (or first threshold) and around here he will have a spectacularly bad shot that symbolises everything that has gone wrong. He will then fight to get back on form. In this sort of story there's usually a big build-up to a comeback match upon which everything depends. Not just the match itself, but also the player's career, his relationship and even his life. This match will eventually hang on one single shot. This shot will obviously be given a lot of status (through the build-up and the way it's talked about and presented – in a movie, it will probably happen in slow motion with dozens of cutaway shots to see people's reactions). It will also be an amazingly skilful shot or an unfathomably lucky one.
Now, whilst scenes should not be about what's happening, but instead the relationship between the characters, stuff should happen. And if that stuff actually reflects or symbolises what's happening to the characters, then this is perfect. In fact screenwriting is all about making stuff happen that illustrates the characters and relationships because we can't see the human brain working, we can only see the effects it has on people, namely their actions. Thus this final bowl isn't about a ball going down an alley. This ball now represents everything: The hero's hopes, dreams, career, love-life and even himself. If the ball makes a strike, the hero regains his self esteem; the girl will love him; his peers will welcome him back with open arms; he'll have the prize money to pay off his debts and not have his legs broken by the debt collectors. If the ball goes into the gutter, his hopes and dreams follow it; the girl he loves will leave for good; and he'll wind up a sorry, broken man, or even dead. It's really not about bowling any more. In fact, it never really was.