Here are some tips to help you level up fast in SWTOR:
1. Doing quests that have multiple stages. You will get extra XP and rewards by doing this kind of quests.
2. Save time. Companions, spaceships and vehicles are very helpful for you to save time. Also you can use your Quicktravel ability. When you finish a round of quests, you should use this ability to port back. Another powerful warp is called Emergency Fleet Pass. The only downside to the Emergency Fleet Pass is that it has an 18 hour cooldown. What you want to do is save this for the end of the night when you log-off for the night. Warp back to the fleet and log-off in the cantina.
3. Doing daily PvP quests when you reach level 12.
How to get the PvP quests?
You have to pick them up from the PvP quest terminal, which is found in the Imperial Fleet (Empire) or the Republic Fleet (Republic). An easy way to get back to the fleet is via the Emergency Fleet Pass mentioned above.
Once back at the Fleet, you can find the PvP quest terminal in the Combat Training section of the fleet. Once you get close you should see the quest pop up on the map.
4. Doing daily flashpoint quest
How to get the flashpoint quests?
You can pick this up from the “Daily Mission Terminal” which is found in the part of the map denoted as “Supplies” on the Imperial or Republic Fleet. This typically gives you two flashpoints to choose from which you can complete for a nice reward.
5. Flashpoints and group quests that depends. If you can join in a group quickly, you can consider this. But if you need much time to get the group together, you can just ignore it.
How To Level Fast in Star Wars the Old Republic – Power Leveling Made Easy!
SWTOR Leveling Guide