To organize or find existing instances, you must locate the quest area and interact with the statue that has the desired quest you wish to complete. Upon doing so, a menu will open, as shown in the image.
If there is an existing public instance, you can simply join by clicking on it. If you want to organize an instance yourself, just click the New button.
After clicking the New button, another menu will appear, as shown in the image on the left.
In this menu, you can select the difficulty level you want to attempt the quest at. The Easy difficulty will have a negative modifier on monster damage and health, as well as reduce the rewards you receive. The Normal difficulty will not apply any changes to health, damage, or rewards, while the Hard difficulty will increase all the above modifiers.
Next, you can choose whether to make it a public or private instance. Public instances can be accessed by anyone, while private instances are available only to those accepted by the party leader (you can also go alone if you wish). Pressing the Create button will send everyone in the party to the quest.
If you created a private instance, it will be displayed in the menu as shown on the right. If someone outside the group wishes to join, they can send a join request, and it will be up to the party leader to accept or decline.