First find one of the quest boards these will be large signs with the name of the quest and tasks on.
First click on the HUD panel to the left. It will give you a folder with a HUD and notecard. Wear the HUD and read the notecard for the quest instructions.
Each quest may have several tasks. As you finish each task come back to the sign and click on the task you have finished. If correct it will tell you in chat that you have completed the task.
Do this for each of the tasks and you get a message saying you have completed the quest and receive a reward for it.
While many quests require you to gather or cook or make something some may simply be to find certain objects.
There is a starter Quest and a sample Quest in the Library and some around the village
REMEMBER!
If you go searching in the Woods and especially the Dark Woods to take a weapon with you! The woods has some animals that will not take kindly to you invading their territory ( only one or two) and the DARK WOODS has animals that are hostile and will attack when you are in range.
More Quests will be added ( or changed) as we grow including Group Quests.