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Location, location, location
The GPS radio is a power-hungry piece of hardware, and if you don't want to know where you are the whole time you can make a change that will save you some battery life.
Tap Settings > Location > Mode and change the mode to Battery saving.
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!).