Setting up an improv scene is not unlike writing a news article. There are some basic questions you're trying to answer to provide a well-rounded picture of what's going on. You could sum up CROW with the questions Who, What, and Where, but I think CROW is a better acronym.
You want to develop a specific character, and help develop your scene partners' characters as well. In order to do this you will need to make some initial choices about how you physically present yourself--what do you look like when you stand, move, speak, etc. And, as a character--the first few sentences instantly define something about who you are. Character is the flesh of the scene--the thing that makes it unique and specific.
If scenes don't establish relationships, they don't touch any sort of human core--and, therefore don't do much of anything. I personally think establishing relationships is what makes things interesting, but it's really just one piece of the puzzle. Establishing relationships requires physical gestures--do you give the person personal space, are you showing open postures or closed postures, are your facial expressions friendly, do you make eye contact? Establish relationships also needs words, and your first few sentences can not only define the relationship, but show what your objective might be in the relationship. Relationship is the central nervous system of the scene--it makes connections and provides meaning, otherwise actors are just robots doing saying things to each other in particular places.
We are not Buddhist monks. Improvisers are not trying to eliminate all desires and act from a blank slate of enlightenment--because that's not interesting to watch. Every character needs some motivation for a given scene. It can be specific like trying to get a good deal on his car insurance, or more subtle like trying to finally feel secure by bragging about all her accomplishments. You decide, but you need some objective--and, the clash or synergy of different characters' motives is the blood of the scene.
Everything happens somewhere. Sometimes it doesn't matter exactly where, but sometimes place is the very thing that causes tension with characters, and provides objective. Ex. You can have a group of gangsters arguing over directions. But, if these gangsters are camping in upstate New York as part of a forced rehabilitation program--hijinks ensue.
Those are the basics. A great exercise would be to set up mini scenes--15-20 seconds, to see if you can incorporate all 4 aspects quickly. Also, be sure to attempt to convey some of these elements through physical actions, rather than being a talking head/narrator (ex. "I am now in the woods, and am an angry man").