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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.
Bin unnecessary widgets and wallpapers
There's no such thing as something for nothing, so get rid of anything you're not using or don't find useful.
Clock on Apps and swipe left to go to Widgets to see what's installed.
Live wallpapers are a far bigger drain on your device's battery than static wallpapers, so if you want the most out of your battery, don't use them.
Tap Settings > Display > Wallpaper to check or change your settings.