Vista jumping puzzles
Most vistas are hidden or put in hard to reach places. If you can't find your way up to one, wait for another player to come by and watch them. They might figure it out first, allowing you to trace their route for yourself. If no one's around, ask in the local chat window. Guild Wars 2 players are mostly a helpful and welcoming bunch.
Most melee weapons have 'chain attacks'. When you hover over the basic attack on your quickbar, you'll see three 'stages'. If you use the ability three times in a row, you'll create a combo and deal extra damage/conditions. This can be interrupted by some enemy attacks.
When you reach level 11, you can buy your first (adept) training book for 10 silver. Look for the green book icon on your map for the trainer specific to your profession. They can usually be found in cities. When you use the book, you can access your traits through the hero menu.
Orange quests are dynamic events. The more you take part, the better your reward. Whenever one flashes up on the map, it's always worth getting involved. The progress bar, unlike regular quests, is collaborative. All players doing the quest add to it by completing objectives. Often these will contain the same objectives as heart quests, allowing you to kill two birds with one stone.
Unlocking weapon abilities
Whenever you switch to a new weapon for the first time, it'll only have one basic ability. To unlock the rest, kill mobs. It doesn't take long to fully reveal all of a weapon's powers, which means you can switch weapons at your leisure without having to worry about wasting time dedicating yourself to one specific type.
Remember to dodge
If you're fighting an enemy up close, don't just stand still like in most MMOs. Double tapping a direction key will make your character roll and evade. The yellow bar above the red health orb is your energy, and you won't be able to evade if it's empty. Some abilities combine an evasive roll with an attack, which is useful if you're low on health.
Be sure you check the 'auto loot' option in your preferences. This means that when you press F to loot an enemy's corpse, the items will automatically be added to your inventory (providing there's space).
Talking to NPCs
Always talk to NPCs with unique names (as opposed to 'farmer', 'hunter', etc.) Often they'll trigger a dynamic event, or offer some other useful information.
The tab key is your friend. When you hit it, it'll automatically target the nearest enemy during combat. If you're attacking an enemy that's further away with ranged abilities, then another mob comes up close, hitting tab will immediately switch your aim to them.
Whenever you complete a heart quest, you don't have to turn the quest in, but always make sure you talk to the NPC with the golden heart above their head. They'll have items on offer that can be purchased with karma points (the purple triangle icon), some of which are of a high quality. There are also 'cultural weapon' karma vendors in capital cities. Once you've hit level 40 you can buy rare weapons/armour from them in exchange for karma points.