Hello
I tried to google it today, but I had trouble even to express my query in simple terms

I have device (Airport express) powered by mains (internal wall-wart outputting 1.21A for 5V and 0.7A for 3.3V).
I'd like to add backup battery power to it - so when
- device is connected to the mains it is powered by wall-wart & battery is charged up
- device is disconnected from the mains power then battery immediately kicks in supplying power to the device
I'd like Arduino to control the charging process & report battery status via led bar.
I don't expect to find ready solution, main steps, building blocks etc?

Image is from here
http://uavbob.wordpress.com/2009/03/25/airport-express-power-supply-repair/