1. Discover and use your Travel Points.
If you are a veteran of MMORPG games then these are very familiar to you. Along the way you will find Travel paths that allows you to travel between locations. Make sure to click on each one even if you don't plan on using them at that moment as they will come in handy later.
2. Click on every bind point.
Unlike other games that only allow you to save one location as a bind point, SWTOR lets you use all of them. Make sure to click on each one you come across so that when you use your quick travel icon you can choose any location you may need.
3. Mission locations may be on another map
Missions (Quests) are displayed on your map to help you find the location you need to go to to complete them. However some are on adjoining maps and are not immediately visible. Doors or portals to other maps will have a list of quests available on the next map.
4. You can heal your companion character by healing yourself.
To replenish the health of your companion simply enter your healing state for you self and your companion will heal as well.
5. Always log off in a Rest Zone
Make sure when you are done playing to have your character inside a rest zone. While there he will gain rested experience which allows you to gain more XP when leveling. Do this enough and it will greatly increase your leveling rate.
Ok so I have one more so just consider this as bonus help. This is also the most asked question on Tython so I thought I would include it.
6. Getting your light saber is not associated with level.
You will receive your light saber once you have completed the mission chain that grants it, not at level 10. So no worries it will come to you soon enough.
Well I hope this helps you some, happy gaming.