A Virtual Desktop widget is available by default on the panel of KDE. Right-click the widget, and you can set the number of Virtual Desktops and name each one for convenience.
Typically, uses reserve each Virtual Desktop for a specific application or set of applications.
For instance, if you are an administrator or a developer, you might have one Virtual Desktop with a command line always open. Another might have your web browser always open, and another your email reader, while a fourth might display other applications. With this setup, a shell, email and Internet are always a click or a keystroke combination away, so you never have to search for them.
However, as implemented by KDE, Virtual Desktops have one problem: You cannot have different sets of icons on each desktop, nor give each desktop a separate wallpaper to make it instantly identifiable as you move around.
Activities are essentially a more sophisticated version of Virtual Desktops. In addition, they can be used independently or in association with Virtual Desktops, so it is easy to confuse the two. I would suggest that users consider Virtual Desktops as a deprecated feature, unless they are used to them. Otherwise, if you use Activities exclusively, you can remove one source of confusion from your computing -- to say nothing of the Virtual Desktop panel widget.
You can create a new Activity by clicking the desktop toolkit, and selecting Activities -> New Activity from the horizontally scrolling window that opens (in earlier versions of KDE 4, you zoomed out to a view of all Activities, which was confusing and often difficult to control because of the small size of the display).
To associate an Activity with one Virtual Desktop, right-click on the desktop and select Folder View Activity Settings -> Activity. By changing the Activity associated with each Virtual Desktop, you can customize its icons and wallpaper to make it more readily identifiable and useful.
However, if you decide to ignore Virtual Desktops entirely, you can select Activities from the desktop toolkit and make a selection from the horizontally scrolling window. More efficiently, you can scroll through all Activities by pressing Ctrl+Shift+N (Next) or Ctrl+Shift+P (Previous).
In a sense, Activities (and, to a lesser extent, Virtual Desktops) do for desktops what Folder Views do for icons -- they remove the restrictions and give users more flexibility.
These are just the most obvious solutions in KDE for the problems of the modern desktop. Many other features also help to address these problems. In particular, the ability to put multiple windows on the tab of a single window, which is available from the menu of any window, is another way to reduce clutter on your current desktop. So is the ability to tile windows by moving them to one side of the screen; you can enable it by selecting Menu -> System Settings -> Window Behavior -> Screen Edges.
Other KDE 4.x features have the same purposes, but are less successful. For instance, the default menu seems designed to reduce the extra clutter created when sub-menus spill out across the desktop as you descend them. However, in this case, the reduction of clutter makes navigating the menu harder, since only one level is visible at a time, which solves one problem while creating another.
Probably the biggest question about the KDE innovations is how necessary they are. For undemanding users, they may be only a needless complication, and something to ignore. Similarly, those long accustomed to the average desktop may feel no restriction in its limitations.
And even if you see what the innovations are supposed to be doing, you may take a while to forget old habits and learn new ones -- I certainly did.
But no wonder what you think of these features, they are what makes KDE 4 distinctive, and not just a refinement of KDE 3. In the end, I suspect that, more than anything else, the verdict on them in particular will determine the verdict on the KDE 4 series in general.
That's assuming, of course, that users can ever understand how they work.