For most English and German angoras you will need to shear the wool off with scissors or a clipper. For French angoras you will need to pluck (pull the wool out of the new coat) either by hand or using a fine comb.
My french are used to being sheared to the skin. I clipped the buck last time, because these guys hold their coats 5-8 mos, and when they molt, they don't really do a clean molt.