Easiest way to switch between running apps is to swipe with four fingers across the screen. Alternatively, you can switch by four finger swiping up the screen and selecting the app from the multitask bar.
To get back to the home screen quickly, place five fingers on the screen and draw them towards the middle of the screen. That will close the app you are viewing, but it will still be available in the multitask bar, and will remain in the same state as it was when you closed it.