Unlike iPhone, there is no task manager for windows mobile 8. But lets hope to have a similar feature in the future releases.
Also unlike Android, most of the memory management is well carried out by Windows itself. So that the background running app doesn't drain much of your battery life. An exception to this is Nokia Drive app on your Lumia phones.
The only way to close apps on Windows Mobile 8 is to press the back arrow button ( ). In case of background running apps, first long press the back arrow button and you get the background apps as tiles. Navigate to the app that you want to kill by clicking on its tile and then close it by pressing the back arrow key.
So the key point here is to close your apps by simply clicking the back arrow from the application.
Its a straight forward process but initially a bit confusing for other smart phone users like an android or iphone.
Summary:
1. Long press the back arrow button to display the background running apps.
2. The press the back button from each app to close them.
Tip:
Internet Explorer works in a bit different way.
For Internet Explorer, it is a little different. If you use the task switcher to get to IE, it will have your history intact. If you had a long browsing session, it could take quite a while to back button out of IE. Instead of using the task switcher, just launch IE again, this will clear your history and a single press of the back button will close it. This is nice when you are about to hand your phone to someone and you don't want them to see what you have just been browsing. Unfortunately it does not clear the recent list from the options menu.