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How do I install a rechargeable battery into a boombox or device that can be charged via ac adapter?

How do I install a rechargeable battery into a boombox or device that can be charged via ac adapter?

I'm building a boombox and want to have an internal power supply that can be recharged via  the ac adapter that comes with the battery.  I want to be able to charge it without having to remove the battery.  

I'm guessing I need to wire in some sort of switch that switches between power mode and charging mode,  but I really have no idea how to go about it or where to find the relevant information on how to do it.
 I'm an electronics noob so any input would be appreciated.  Thanks