Leveling up in Guild Wars 2 works pretty much the exact same way it does in every game. You can kill mobs, do quests or other events like dungeons and such to gain experience when the usual solo grind gets boring. It's a whole lot different with GW2 though because the solo grind combines all of these things together and they work in quite an awesome way. All of the quests in the game are area quests where you can do multiple different tasks to complete the one you're working on.
What I mean by this is you can say kill a bunch of thieves who are stealing from a town or take back the supplies they stole or place traps to complete the quest. It takes away from those quests you usually always hate to do and gives you the opportunity to do quests the way you enjoy doing them. Now depending on your class and what makes you comfortable while playing there are quite a few different recommendations I would like to make early on. Since A lot of the harder classes that require you to be constantly on your toes and have gear equal to or above the level of mobs you're fighting.
Before I get started with the rest of the guide below is a video covering exactly what I do to level my ALTS. Please keep in mind you won't have the money to level your first character this way, however if you get level 80, get some cash and really want to play a different character or just have an alt the information in the video below will be the fastest possible method for leveling.
These are a few Guild Wars 2 Leveling Tips that I think new and current players alike will find very useful to assist in leveling.
1. Backtrack and do other 1 - 15 zones after you finish your 1 - 15 zone.
2. Upgrade your gear every 10 levels. 5 is too minimal and you'll end up spending more money than you should.
3. Don't forget to spend Trait Points! Press (H) and then select "Traits" to access this tab.
4. Don't forget to gather the materials you come across in the world. Even they give experience!
5. If you really want to skip a level bracket Crafting helps a ton (see video below)
6. Join in on any active Events, especially at higher level. Events will get you a ton of kills as well as a large amount of experience or Karma at the end! Even if you see an active event that you don't want to finish kill a few mobs that way you'll at least get a Bronze Medal which is still 2 - 3k XP!
7. WvW (War vs War) is also a great source of experience but it can be a lot more random than doing things like events. Getting good XP in WvW means you need a competant team that knows what they're doing. Or you can hope the enemies team is even less competant than your incompetant team.
That's all I can come up with now but if you check back later I am sure I will be adding more tips over time! The main point I am trying to make, however is that Guild Wars 2 is an extremely easy game to level in. I got to level 80 in about 4 days time and now that I know what I know now I bet I could do it twice as fast! The best piece of advice I can give you though is don't rush to 80 in Gw2. Since the game has this system where it lowers players to the highest level for that area most players aren't even playing at level 80 with all of their best stuff at 100% (unless you're in WvW).
What that means is even if you're level 50 in a level 30 area you should be able to do just as much as a level 80 in that level 30 area. Of course player ability plays a huge role here but from my experience it seems to work out just like this.
Crafting for Experience (70 - 78 in no time!)
Believe it or not crafting gives some of the best experience available in the game. You can get an unreasonably high amount of experience from Crafting, more experience than you could get in a shorter time than doing anything else out there, actually. You can see what I mean in the video below. If you really want to get a good amount of experience with Crafting wait until you get a Crafting Booster from a Black Lions Chest and then figure out all of the materials you need before going all out.
If you need some good Tradeskill Guides feel free to check out mine, they will be able to provide you with a lot of the information you need for raising your Crafting.