The entrance to Forgotten Wastes is just next to the main road. You can’t really get lost here, as it is not as wide as you might think it is. The dungeon’s front door is part of a larger building, the one with high towers. In the southern part of the island we have mushrooms, and here we have this type of towers.
At the start of the dungeon, you can accept the quest “Echoes of a Fallen House” from Tythis Nirith. The first step guides you toward the second room, where we are headed. Just go south in the first dungeon area, and find the Caverns of Koguruhn.
The skyshard is inside the Caverns of Koguruhn, just north from the lava, on top of the higher level platform. There is a small wooden beam that leads to it, so be careful with the steps. You won’t be grateful for the fall, especially when you want the prize right away.