I understand that he takes them as trophies from defeated opponents, but how does he get his first one? Does he defeat a Jedi without a lightsaber (who?)? Or is he given one by a Sith?Does he make his own (without force assistance)?
According to Wookieepedia, Count Dooku presented him his first lightsaber:
This information comes from 14-page comic The Eyes of Revolution, from Star Wars: Visionaries, in which a fully cybonic "Sheelal", wounded and mind tempered with, receives his first lightsaber from Dooku (reporting to Darth Sidious) and, after reacting with anger and violence at being called a "droid", announces himself to be General Grevious.