To be able to enter the Dorgeshuun mines, you must first have completed The Lost Tribe quest. Once you have completed the quest, you can enter the caves - although you require a light source of some sort. To enter the cave, head to the basement of Lumbridge castle and climb through the hole you made in the Lost Tribe quest. Find Kazgar, and ask if he can show you the way to the mine - you will automatically be dropped there, free of charge. The quest Wanted, also takes you into the mine. For more information regarding mining here, see our Dorgeshuun Powermining guide.