The big obstacle is Metro, which runs on only one display at a time -- by default, the primary display. There's no way to have the Metro UI span more than one screen. That said, you can move Metro apps between displays, just by moving the Metro desktop itself. If you have Metro visible, press Win-PgUp or Win-PgDn to move it between displays. You can accomplish the same effect by clicking near the top of the Metro desktop when an app is open (you'll see the cursor turn into a hand) and dragging the app between screens.
The black margin at the bottom of the left-hand desktop is due to the difference in the size of the two displays (a notebook with an external monitor plugged in). (Click for larger version.)
The way the taskbar behaves in Windows 8 is also important. If you have the legacy desktop duplicated across both screens, the icons in the taskbar are duplicated across both screens. This can be a bit confusing at first: For example, if you go to screen 2 and click on an icon for a minimized app that was on screen 1, it restores itself on screen 1, not 2. On the plus side, wallpapers can now span multiple monitors, so now you have an excuse to dig out that panoramic picture of Times Square you snapped last year. (Select the Span option for Picture Position when you select a wallpaper.)
A dual-display Windows 8 system with wallpaper that spans both desktops, which is now possible natively in Windows 8. (Click for larger version.)
Charms work on all monitors as well, but be careful of the way the edges of monitors that have been set to appear side by side flow into each other. With a single monitor, you can flick the mouse all the way to the right edge of the screen, have it stop there, and have the charms bar appear automatically. If the right edge of that screen leads into the left edge of another monitor, you'll need to slow down and feel around a bit for the charms bar to appear.
The sensitivity of the bar's appearance has been tweaked since the early Windows 8 alpha releases, so it requires a lot less fidgeting to invoke. But as noted above, using keyboard shortcuts like Win-C spares you a lot of pain.
Managing windows in Metro mode Metro is only meant to run one app at a time, which stands in stark contrast to most users' typical way of working on Windows, with multiple windows open side by side or on top of each other. To ameliorate this shortcoming, you can "snap" a Metro app to run in the margins of the screen, while another Metro app -- or the legacy desktop -- runs in the remaining space.