Here is the battery I am using:
I check via a multimeter if there is still life in it. If its dead I just swap it with the other one I have on charge. (saves cash!!)
As for the setup. Please refer to my description in a post above. I have the 9v on the power rail on the breadboard and the servo is wired into that. Ground is also on the same power rail and it is wired to the gnd pin on the arduino. The signal is from the breadboard (yellow wire from servo) to D9 on the arduino.
Hope that makes sense?? Actually hard to describe in detail with words.