To hook your batteries up to the arduino board you just need a voltage divider to scale their output voltage to the dynamic the arduino is expecting. Depending on the board you are using it should be 3.3V or 5V. And of course the arduino board should be powered with a well regulated power (not the battery).
Concerning the time left it is all but simple. It is function of battery charge level and current consumption. If you want an accurate value, at any time, you need to know how many charges remains in the battery and how many current you are consuming. For a simple display you can use the voltage. But be aware that on many batteries the voltage stays at nearly the same voltage for all the discharge cycle and suddenly ramps down.