Shutting down running apps in iOS I often have many apps running in the background. I have heard this can cause the battery to drain faster (especially location-aware apps) as well as generally slow the use of the device down.

Is there a fast and easy way to shut down all running apps in iOS?
You don't need to.

See 
iOS Multitasking in Detail
and
iOS: Understanding multitasking

Basically, if you're using an app (you can see it on your screen) then you're app is running. When you press the home button and leave the app or switch to another app then the app is NOT running. It may be in one of a few other states (see first link) but it is not consuming any processing power or memory. There are very few situations where closing the app will save you any time or effort and it's best forgotten.