Reveal map with scouts
Look for the telescope icon on your map. This is a scout, and talking to them will reveal a large area of the map and give you details of the heart quests in that area. You can also uncover the map (as well as waypoint, vista, etc. icons) by simply walking there.
Claim your rewards
When you complete a quest, you'll receive a mail from the quest giver containing an amount of coins. Remember to click the 'take all' button to claim it. You can delete messages from your inbox, but don't worry; the game won't let you delete mails that have an attached reward.
Your level is dictated by the area you're in. If you're a level 60 character and you decide to go questing in the starting area for one of the races, you'll be reduced to the same level as the newbie players there. This means you can still take part in quests you missed/skipped and it won't be a waste of time. You'll still get appropriate XP and loot for your level. To find out if your level has been reduced, look at the bottom left of the screen. The green number is your adjusted level.
If you're wondering why you can't find your friends, or why the chat window is full of all different languages, you're probably in an overflow server. Look at your mini-map under the area name. If it says 'overflow' then you're in a multi-language 'holding' server, waiting for a space to free up on the real one. Once you're in properly you can meet up with your buddies.
At the bottom right of your hero screen you'll see your underwater gear in blue. Upgrade these as soon as you can, because the starting gear is weak. You can buy harpoons or spearguns (depending on whether you prefer ranged or melee combat) from weaponsmiths or karma vendors. Better breather masks also come with minor stat boosts.
Hide the interface
You can disable the HUD for taking screenshots. To do so, press ctrl+shift+H on your keyboard. Pressing the print screen button will dump a shot in your Windows docs folder in .jpg format.
To activate gathering nodes you'll need a sickle, pick, and logging axe. You can get these from vendors, and they're equipped on the hero screen just under your accessories. Better tools allow you to harvest better materials. Even if you don't care about crafting, it's still worth harvesting things. Trees will occasionally drop minerals (nuggets, pebbles, etc.) that you can add to weapons and other gear to upgrade them. Chop every tree you see out of habit.
Draw on the map
Hold shift and left click on the map to draw on it. Party members will see your lines (which fade slowly) which you can use to plan out your questing route or highlight secrets.
Share items between characters
Your bank is account-wide. This means you can dump items in it as one character, then retrieve them as another. You can't mail items directly to your other characters, though. There's no in-game trading, either. If you want to give a party member an item, just mail it to them.
Buffs and debuffs
Boons are status effects that benefit your character. Conditions are negative status effects. An example of a boon is fury, which gives you a 20% critical chance increase. An example of a condition is bleeding, which inflicts a set amount of damage per second. In more common MMO terminology, these are basically buffs and debuffs. You can find a full list of conditions here, and a full list of boons here on the official Guild Wars 2 wiki.