To construct your first lightsaber, you will need three components and a crystal.
Fastest method to assemble your lightsaber.
As soon as you leave Telos travel to Nar Shaddaa. Once there proceed into the central area and find the zoning door to the Docks. Halfway across the Docks will be a door that leads to the Flophouse. Go to the end of the hallway of this flophouse and the second to last door has a guy named Lootra. Taunt him into attacking. (This could cause you to lose influence) His corpse will have a lightsaber part. Next if your alignment bar is about 25% good or bad you can return to the Ebon Hawk for a special fight which will get you the last lightsaber part. If you are not 25% good or bad there are tons of things to do in Nar Shaddaa to get the last of the points you need.(If you do not have a colored lightsaber crystal the merchant Geeda will have one you can buy so don't scare her away) Now talk to Bao-Dur to have your saber made.
Also check out Dantooine, you can slaughter/buy the parts of the salvager trapped in the enclave. Dantooine also has the crystal you need for
Doing the story quest on any planet after Telos will probably give you all four parts. Then, talk to Bao-Dur to craft it.