The pager gadget on the shelf shows small graphics of the available desktops with the applications running in each.
There are several ways to switch among them:
The screenshot here shows two instances of Terminology, one that is Shaded and one that is not. Terminology is provided by the optional terminology package.
Alt+<left-click> (mouse)
allows you to click anywhere in the window to grab it and reposition
<left-click> (mouse)
on an open portion of the desktop, opens the Main Menu
<right-click> (mouse)
on an open portion of the desktop, opens the favorites menu
Ctrl+Alt+X (key)
closes a window
Ctrl+Alt+<ArrowKey> (key)
switches to the Virtual Desktop in the direction selected
Ctrl+Alt+M (key)
brings up the Main Menu
Shift+F10 (key)
maximizes a window vertically
Alt+Shift+F10 (key)
maximizes a window horizontally
Alt+Tab (key)
switches between windows on the same desktop
For more information and a comprehensive list of all default keybindings, see Bodhi Wiki.
You can open the Quick Launcher by clicking its gadget on the shelf, or by pressing the key bindings Alt+Esc or Ctrl+Alt+Space, or from Main Menu -> Quick Launcher. It will close automatically after performing the requested action, otherwise close it by pressing Esc or clicking outside its window.