Firstly, speak with the Observatory Professor, located in the Reception Room of the Observatory. Ask if you can look through the telescope, and he says that it's broken. He tells you that a family of Goblins has tampered with the telescope, so ask if you can help. He says that he needs some wood for the Tripod, bronze for the Tube, and glass for a new Lens.

 

You can find the 3 Planks needed to fix the telescope just north of the Barbarian Outpost, which is to the far north of Ardougne. A Bronze Bar can be Smithed by anyone, or you can buy one. A piece of Glass can be made by using your Crafting skill. Once you have these 3 items, bring them back to the Professor who will take them from you. He then says that he needs a mold so that he can make a new Lens.

 

Now go down the ladder in the Reception Room to find a cavern. From the ladder, head east and then north. Follow the passage west until you come to a Keep Gate guarded by a level 42 Goblin Guard. Run past him to the north, and follow the twisting path to the west, and then south. Now, take the west path and follow it southward until you come to a small room with several passages leading from it. Take the southeast path and follow it until you find a chest. Open it up, and then search it to find a "Keep Key".

 

Now that you've got the key, head all the way back to the Keep Gate that you passed, and attack the Goblin Guard. After killing him, use the key with the gate to unlock it, and then search the sack next to the table to find the Lens Mold. Bring this back to the Professor, who now says that he doesn't have a high enough Crafting level to make the Lens for the Telescope. He gives you the Glass and the mold back, so just use the molten glass with the Lens Mold to Craft him a new Lens. Give it back to him, and he wants you to visit him in the Observatory.

 

Climb back down the ladder into the maze, and head all the way back to the small room with all of the passages leading from it. Now, instead of taking the southeast path, take the northeast-most passage to find a ladder leading to the Observatory. Talk to the professor, and then "Use" the Telescope to see a constellation. After closing the window the Professor should talk to you again. You can choose either option, and you should get your reward in your Backpack!

Rewards
Your item reward depends on what Astrological Sign you see when you look through the Telescope and it is also different for each person.
The Spirit of Scorpius will now give you a mould to make Unholy Symbols, and he will bless them for you too. He can be found in the graveyard north of the Observatory.
2,350 Crafting Experience
2 Quest Points