Out of all the pages I have for helping you to quickly level in Swtor this is the most important one for you to read. This doesn't have anything that will dramatically speed up leveling like some sort of cheat or a secret grinding/questing place. This page has more common knowledge type things that will greatly improve your leveling speed if you know when to use them and just plain know that they are there. Anyway, without further ado, here are some of the ways for you to quickly and easily improve your leveling speed.
Many people don't know about this but your Companion is able to sell all grey items which you find while killing monsters and grinding in Swtor. You get a companion in the very first few levels of the game regardless of what class or allegiance you choose. The companion window is in the bottom left of the screen and curently can't be moved. In order to get your companion to sell your items what you need to do is click on the little button in the upper right hand corner of his picture, it looks a bit like a spaceship if you ask me. (A picture of what you need to click on is above, look for the little blue arrow pointing to it in the bottom left)
Once you click on this little icon it will bring up a large window above the companion frame. Here you will see all of your companions and their abilities and what not. To get him to sell your items what you need to do is click the icon in the bottom right of his information frame that looks like (#7) If you click on this then from there you can easily figure out how to send him off to sell your items. Once he leaves it will take about a minute for him to go sell the items and come back to you. While waiting for him you can either continue questing/killing mobs or take a quick afk. It is up to you!
I recommend getting all of these as early as possible, which is right around level 9 or 10 when you leave the noobie areas and enter the main towns for whatever faction you are on. The Tradeskill NPCs are quite easy to find if you know what you're looking for. On the minimap they will appear as little Diamonds, and you can find them all over in the section of the town they are meant to be in. I say meant to be in because in each city if you hit "M" there will be a section dedicated for Tradeskills/Crew skills. This is where you will be able to find these guys.
If you can't find them on the map you can always ask for directions in /1 or ask a friend or of course just run around aimlessly. Either way it is quite worth it to collect all of the Codex entries for these Tradeskills because each Codex entry gives you something like 450xp. In order to acquire the Codex entry all you need to do is simply right click the trainer and it will automatically reward you with the entry and grant you the xp. I'm not sure if the XP scales with level but either way I still recommend doing them all right at level 9 or 10 since after collecting all of the entries you will be about half a level higher than you were.
Much like collecting Codex entries for Tradeskills, this section will go over collecting Codex entries for just about anything. Codex entries are quite easy to find in the world of Swtor if you keep your eyes open. What you need to keep an eye out for are objects that are glowing blue, much like the box in this picture above. When you right click and inspect one of these objects it will add an entry into your Codex and grant you a certain amount of XP depending on what you scanned. Collecting Codex entires certainly won't help you reach max level dramatically faster than usual, but it certainly will help you.
At least early on in the game a single Codex entry is worth about 450xp and each mob you kill is worth anywhere between 75 and 114xp, depending if it is a "Strong" mob or not. In the time it takes you to kill four mobs, you can easily collect a single Codex entry and be on your way. In other words what I am saying is they are definitely worth going slightly out of your way for. Even if you're not interested in the extra xp for each entry, at least inspect it so you don't regret missing it and having to go back for it later.
This is the most important thing to keep in mind and to do when it comes to leveling faster in swtor. Doing each and every Bonus Quest you come across will vastly improve the amount of XP that you earn on an hourly basis. Now not all Bonus Quests are easy to come across and a lot of them require you to go ever so slightly out of your way to kill the right mob and trigger the quest. By the time you reach level ten you will understand what I am trying to say about Bonus Quests. During most quests killing a mob or doing some hidden objective will trigger a Bonus Quest.
Bonus quests are quests you will be given by doing an unlisted objective while already on a quest. For example, say you need to collect flowers for Juliah, that's the only objective that the quest shows you. But in Juliah's garden are giant wasps which are in the way of you collecting any flowers for her. You won't immediately be given the bonus quest for just being in the area but when you kill one of the wasps it will pop up and let you know that you are now on a bonus quest as well. Bonus quests are not required to progress the story in any way nor have I ever seen them lead to anything important.
The above paragraph was taken from my Bonus Quests guide page. If you would like to view this page click here.