Question: how vader got his lightsaber?
Answer: History. Darth Vader wields his lightsaber. When he originally joined the Sith, Darth Vader simply continued wielding his second lightsaber that he created as Anakin Skywalker. However, this lightsaber was taken from him by Obi-Wan Kenobi after his defeat at the Jedi's hands on Mustafar.