Required:

Items: 1 gp, bucket/jug of water (bucket can be obtained in quest) and 25 normal bones (cannot be noted)

Monsters: Delrith

1: Acquiring the sword:

Go north from the tent into the castle, if you go a little North-west you will see a man named Sir Prysin, the person who is supposed to have Silverlight. He explains the Silverlight situation to you and sets you off on a quest to find 3 keys.

2: The First Key

The easiest of all, go to the NW corner of the castle and go up the staircase twice, talk to Captain Rovin and he will eventually give you the key.

3: The Second Key

Go to the castle kitchen (northeast corner) and go through the door to the courtyard and just to left of the exit you will see a drain. You will need a bucket of water, you can find a bucket by climbing the stairs in the kitchen, use the bucket on the kitchen sink to fill it with water. Use the bucket/jug (with water in it) on the drain and the key will fall into Varrock sewers. To get to the sewers, it's the (!) symbol on the map, east of the castle. The key is on the North-western path.
Note: There is a bucket respawn just upstairs above the palace kitchen.

4: The Third key:

For this one, you must make your way to the Wizards Tower, which is south-southeast of Draynor Village. Stop at the bank to get your 25 bones (or kill any easy monster like Chickens or Goblins to get them), as these are needed to get the third and final key. Once there, go up the stairs and talk to wizard Traiborn. You can also fight the wizards in the area for bones.

5: The Fight:

After you have gotten all three keys make your way back to Varrock castle and talk to Sir Prysin and he will give you the Silverlight Sword. Now make your way to south of Varrock (you should see a stone circle) recite the incantation (this varies for every player) and fight Delrith.