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One of the most effective ways of prolonging battery life is to disable the cellular and wi-fi radios, and you can do this easily by putting the device into Aeroplane Mode.
Swipe down from the top-right and tap Aeroplane Mode.
Install a battery monitor
I use Battery Widget Reborn because it doesn't seem to contribute to draining the battery it is monitoring and it has an automatic night time airplane mode setting, but there are loads to choose from (just make sure it doesn't make the problem worse!).
Dump unnecessary apps
Tap on Settings > Apps and swipe to the left to get to Running.
There you'll see a list of apps that are currently running and you can tap on each one to see what they're doing, and you can stop any apps that you don't need running in the background all of the time.