Nowadays leveling in Wildstar is extremely fast and pretty easy. Even if you are doing all tasks and quests, learning all the story - you will soon hit the wall of doing quests lower level than you. There are near 100 hours storywise quests and content to do if you want learn everything and not rush. And if you rush - you can get to cap in 6-8 hours.
Next tips are for people who want to rush or want to do only main story without learning all the side stories:
Skip all the Tasks. Tasks are special sidequests which have special category for them. They are almost not giving you experience and they are all about helping people in the zone you currently in. They are good if you want to learn about current place, about culture of different species, and so on, but they are not helping you with your main quests, story line and experience gain. Maximum experience you will get from World Story Quests.
Do quests of your level or higher, skip quests which are lower level than you. Main story is separated on many arcs, and you don't need to finish previous arcs to go further and get new main sotry quests. If you don't know where are zones with level you need, you can press N to open Content Finder, there you go to "PvE" tab and there you select "Quests" section.
The fastest way nowadays to get up to level 35-37 is - to spam Normal Dungeons. The secret about them is easy - find one other low character, make a group with them. And after that spam into Nexus chat (it is /n command to write there) with messages "LF X M Random Normal Dungeon!", where X is missing quantity of people to full group (five). If you have already 4 players in group and you see that you all have less than 40k health, you wanna write "LF1M level 50 for Random Normal". People on level cap daily need to do lower random dungeon to get their violet bonus, and the lower dungeon is - the happier they will be (as it can be cleared faster). This way will give for level 50 player - 25 gold per run as well, so you can get some money for your friends on level cap. To start random normal dungeon you want to press N (Content Finder), there you go to "PvE" tab, there you pick "Dungeons" and there you set checkbox "Random Dungeon". Don't forget select your role (tank, heal, dps), better to select all of them. And after that you press "Join as Group" green button. Level 50 player need to be group lead to queue for "random normal".
If you see some "LFM Random Normal" you can join them as well. In Wildstar you just press on name of the poster in chat with RMB and "Join Group". You don't need to whisper or ask anything to join, it is not bad attitude to do that (in most other MMO it is, but not here).
After you hit level 41 - the fastest way to level up is to do Gauntlet expedition on a golden medal (golden medal will give twice experience silver medal will give). Perspective Addon very useful here for finding all the hidden golden skulls flying in the air. You can start it solo, but best way is to do it with two players. To do that, you should set chexbox "Do not find others".
When you hit level 48-49, you should go to Arcterra or Crimson Badlands. In Arcterra you want to find Pillars of Kel Havik event and afk there (you will get experience just by being nearby if someone else finished it). If it is not on cooldown - say into Nexus /n chat "Kel Havik is up!", someone will come and do that most likely. Few this events and you are level 50 (cooldown on event is 15 minutes). Between Kel Havik you can do non-combat events, they are giving nice experience too. Crimson Badlands is a bit different, you should do there some easy questing, it will take you a bit longer, but if there no players in Arcterra (night time or raiding time) it is good alternative. You can get there from your Capital Spaceport, there few helicopters which will deliver you to those specific zones.
If you feel that you are not powerfull enough for your level - do Challenges on this zone. Better on silver or gold, and take "Gear Bag" there as reward. It will give you some item of 1-2 itemlevels higher than zone you are in. It is the fastest and easiest way to have gear up to date while leveling.