The first lightsaber type will be the one you start with.
The second lightsaber type is the double sided lightsaber, this can be picked up by interacting with any lightsaber table in the open world.
The third lightsaber type will be unlocked after traveling to Ilum in the story.
Once you have all three types simply find an enemy with enough health to survive a fair few hits then use each 3 types.
Types one and two can be swapped between by pressing
on the D-pad. The third type is activated by pressing