A: You earn Light side or dark side points based on the moral choices you make in both your story and other dialogue-driven quests. You can get a few titles going further down the path and unlock some items on the fleet. Located in the inner ring of the supplies section on the fleet. One will ask for credits while the other asks for light or dark side tokens.
To get the tokens you can level up a renown rank (Prestige rank essentially after lvl 75) and that will give you 1 token for the side you are aligned with or you can hunt down Light vs Dark world bosses that are VERY powerful and give the token for the side that lost the light VS dark.
To check on the progress in the galaxy map in the bottom right of the screen. Once a side wins it will last for 12 hours. Then it resets to neutral.