Can I power a 9g servo from an arduino nano with USB power only?
The max current of the Arduino-Nano 5V Pin is 200mA. So if you draw more than that it might damage your Arduino.

Here is an interesting summary regarding the Maximum Ratings of the Arduino Nano: https://electronics.stackexchange.com/questions/67092/how-much-current-can-i-draw-from-the-arduinos-pins


  The 5V pin of the arduino is not connected through the
  microcontroller. As such, it can source significantly more power. When
  you are powering your arduino from USB, the USB interface limits your
  total power consumption to 500 mA.


So yes, it actually seems you can draw 250mA out of the 5V PIN.


  do I use the VCC or the +5v?


You use +5V, because VCC is for powering your Arduino with an external Power Source. It allows you to use up to 7-12V (recommended), or up to 6-20V (limits).


  does it matter which ground I use?


Doesn't matter


  should I use a breadboard to help me place any other components that may be needed, i.e. a capacitor or something?


A breadboard makes it easier for you, to test your circuit. But you can do it without if you like. Then you possibly have to solder some connections

See also the offical Arduino Page for the Nano.