I had the joy of this experience when in high school with our three dogs (border collie and 2 labs). One of the labs would just not leave the porcupines alone! Lucky me I was the only one with the stomach to do it.
Best thing I found was wearing tight fitting leather gloves and using locking forceps attached to the quill as close to the base as possible, and need a helper to hold the dog (someone who the dog likes!). Talk to the dog in soothing tones during the whole ordeal, believe it or not this seemed to make a difference. Then some good old hydrogen peroxide generously poured over the area to clean it up.
Best of luck to you. Don't forget protection. :footballhelmet: