I seem to be having a problem with my Metro Skype app. It works fine, receiving and making calls when I have the app open, however if I am using another application (desktop, news, etc) Skype won't notify me of the incoming call or IMs.
I couldn't get Skype to run in the background, but I did manage to open Skype and another task like the desktop at the same time, so maybe that would work for you? Here are my steps:
1. Go to the windows 8 start menu, and select any icon. (If you are using classic shell, your computer might already have the desktop up, so you can just go straight to the 2nd step.)
2. Put your cursor at the top of the screen as far as it can go, and the cursor will turn into a hand. (If you're on the desktop and have something like Word or the internet open, you'll have to minimze it first.)
3. Click the mouse and the hand should do a little grabbing motion, and you can now pull the screen down. It will get smaller. Mine showed up on a navy blue/purple background.
4. You can now either pull it to the left or the right depending on which side you want your desktop on. When you have it over far enough, a line will appear with three dots on it. You can now let it go, and it will stay in that box.
5. Click the remaining navy blue/purple space. It will take you back to the start menu.
6. Pick a new icon. This will cause the two tasks to appear side by side.
7. To adjust how much room either task has, pull the bar with the three dots that separates them.
Hope that helps :> Also, if you want to remove one of the tasks, just pull the bar to the edge of the screen. It will basically shove that task off the screen, and the remaining task will maximize.