I'm a Charr Engineer, so tips for this class are specifically welcomed.
For your first character doing heart events, farming every tree, mine, plant you come across and always dropping what you are doing and helping in dynamic events is the fastest way to level.
The greatest xp/time are events so if you can find continuously repeating event chains that is the fastest way to level outside for a first time character.
Leveling a crafting profession to 400 gives you ~10 levels (this xp is percentage based, so it always gives you 10 levels, regardless of what level you started at).
There are 8 crafting professions, and a the max level is 80, so if you have the mats, you can hit 80 from 2 in under an hour.