Speaking to the King
Speak to King Roald to start the quest. He has a quest for you: light the beacons in the new beacon network to help secure Varrock. He will ask you to speak to Blaze Sharpeye, the finest fire tender on this side of the River Salve whom is located near the Temple of Paterdomus.
Blaze is located just south of the temple which you visited in the Priest in Peril Quest. If you forgot how to get there: Head out the eastern gates of Varrock and head northeast until you reach a little path going due east. Follow the path until you reach the temple; head south.
Head over to Blaze and speak to him about the Beacon Network. He will explain to you about the emergency beacon system and then will ask you to help light a few of them for him for testing purposes. All you need to do is put in twenty logs of the same type on a beacon and set it on fire with a tinderbox. He will ask you to light the beacon now. Use your logs on the beacon and then use your tinderbox on the beacon.
Speak to Blaze again and he will ask you to light the beacon to the west. It is located near a limestone quarry and is just west of the Rag and Bone Man's hovel.
Lighting the second beacon
Head over to the second beacon, by the Rag and Bone Man, and speak to Squire Fyre. Tell her about the testing you are doing and she will tell you to go ahead and light the beacon. Light it like the first and report back to Blaze. He will ask you to top off the beacon there with 5 logs since it is dying off. Tell him you will do it. Place five logs on the beacon and speak to Blaze again. He will talk to you about the beacon network needing more testing. Head back to King Roald after the conversation is over and...