The Discworld's Quest system is fairly simple- you must finish a task, for a reward. These rewards vary; while all quests carry a title and experience reward, some also bestow weapons, money or other spiffy items upon the player.
While quests are not labeled as such, an observant player will probably be able to spot them; because a quest involves completing a task, the player must simply look for tasks to complete!
An example quest (which has since been removed from the game) was the Quest of the Womble's Brooch. Before the introduction of Pumpkin Town, the Newbie Area was a much simpler collection of rooms; wandering these rooms was a womble. She (for, indeed, it was a she) was obviously distraught, and would periodically sob and proclaim that she'd lost a very important possession- her brooch.
The newbie player would, in his travels, eventually stumble into the Hints room, in which (if he read room description) would find that a glimmer of light in the corner caught his eye. Searching the room would result in his picking up an item called a "womble brooch." Giving this item to the womble would cheer her up and allow the player to leave Newbieland.
While many quests on Discworld are much more complex than this, the concept is the same- there are things to be done, and the player must take it upon himself to do them!
This Wiki DOES NOT, as a matter of policy, provide quest walkthroughs, but players may log into the Discworld MUD's website and view the quest files there.