Quests, are available from any kind NPCs, just click the button above and look for the button 'Quest', and that's all. Have fun doing the Quests.
Special Quests, are available in a Special Event. Like Nythera's Marriage. Also some of the Special Quests ends with a large exp amount. In Nythera's Marriage, the last Quests from the event gives you 1000 exp. And also 1000 gold. BUT, make sure you level is high, or you get killed or also make sure that you see a user with a high level. Because they CAN help you.
Daily Quests, you know that already, that means everyday you can do some Daily Quests from the NPCs.