Please see Instance List for a table of all Instances, by the zone they are found in, and the quests that are involved with them.
When you enter the world for the first time with a new character you get the chance to enter the Tutorial instance. You will see a dialog that pops up when you enter the game for the first time. Press Accept and you will enter the Tutorial Instance.
The only quest in this zone is Defeat the Spiders. The quest Three Fungi Brothers used to be in this zone, but it is no longer in-game.