Hi, levelling up happens automatically, if you look at your Health/Action bar there is a circle on the left which states your current level. Now if you want to check your progress to the next level then look at the yellow bar at the bottom of the screen, if you mouse over it you can see the amount of XP you need for your next level.
The profession tree works a little differently, you get 5 expertise points at level 10 and then 1 point for every 2 levels you gain, 45 in total at level 90. You can spend these points any way you wish on the three (2 profession, 1 Beast master) trees, this is where you are meant to gain some individuality in your 'iconic' profession.
As for levelling up/gaining xp your doing the right thing for now, keep questing, even though the legacy can get boring there is enough xp to get to at least level 50. Then head to Kashykk, then Mustafar and you should be close to 90, and don't forget space because you get 9% (more if you have a buff) of your space xp added to your ground.
Hope that helps and good luck.