Speaking to the Priest of Guthix
Speak to the Priest of Guthix and he will explain to you the history of the phoenix. He will then ask that you help revive it as it is close to dying off. After this conversation you will have the option to ask any questions about the phoenix that you might have; ask about the ritual and he will give you the tools you will need. You must collect five twigs to be able to perform this ritual: Cinnamon twig, Sassafras twig, Ailanthus twig, Cedar twig, and a mastic twig.
Resurrecting The Phoenix
As you head through the corridors of the cave you will find a tree in each of the rooms; collect a twig from each tree. Once you reach the last room use your knife on the twigs to make them ribbons. Head into the room where the phoenix is and use the ribbons on the pyre. The Phoenix will then walk onto the pyre. Now perform the ritual by using the tinderbox on the pyre and burning the phoenix to ash.
The Phoenix will soon resurrect from the ash; speak to him and he will thank you with five of his rare quills.
Leave the cave and speak to Brian Twitcher which was formerly known as the Priest of Guthix. He will tell you he saw the whole event and then reward you.