Did you follow the part about why nothing is showing up in your view that is set to Existing and filtered to display Previous + Demo?
Well, you have no elements existing in the phase previous to the Existing phase. And you haven't demoed anything in the Existing phase.
So the expected workflow is to create all the existing model in the Existing phase. Then move into a view set to the New Construction phase and start doing the real-world work, demoing out existing stuff and modeling new stuff.
Now you can add additional phases in the order you would like, but the relationship between them follows the same pattern. Demo should not be it's own phase. It's work done IN a phase just like adding a new wall is work done IN a phase.
I've described demoing stuff that is in the Existing phase while you are viewing the model in the New Construction phase. Enlint talked about demoing stuff that is in the New Construction phase while you are viewing the model in the same New Construction phase. You've modeled a new wall, and then demoed it, all in the same view set to the New Construction phase. Then in that case, like Enlint said, it's a temporary wall that you put up during construction and then took down again. Like maybe a dust barrier or sound barrier.
So you would have duplicated views for your drawing set.
You might have a view only showing the existing conditions. Phase = Existing and Filter = Show New. So it's only going to show stuff you modeled in the Existing phase. Or Phase = New Construcion and Filter = Previous. So it will show the same stuff, but halftoned or whatever according to your phase settings (see the chart Enline showed).
You might have a demo plan. Phase = New Construction and Filter = Previous + Demo. Get it? It's not going to show stuff that's in the New Construction phase that remains. It's only going to show the Existing phase (because that's the previous one), plus whatever you demoed in here the New Constructio phase.
Then you might have a plan for the new work. Phase = New Construction and Filter = Previous + New. See, it's going to show the remaining, undemoed existing stuff (halftoned or whatever according to those settings) along with the new stuff that gets built.
It might make more sense if the Phase Filter parameter used the word "current" in place of the word "new."