Start by talking to Drezel in the dungeon under Paterdomus, the Temple on the Salve, and ask him if there is anything more interesting to do there. He will ask you to take some food to Filliman, found in the Mort Myre swamps. Head south and exit into Morytania.
A note about Ghasts: Ghasts are normally-transparent monsters found only in the Mort Myre swamp. There is a chance for them to attack you; they can either miss, or spoil food in your inventory. If you don't have any food, they will hit your Life Points directly.
From there, go south and look for a gate into the swamps. Don't forget your amulet of ghostspeak, and head into the swamp. Head to the far south of the Mort Myre swamp, and look for a little island. There is a broken bridge you can jump across on the south side.
Try to enter the grotto, and a shifting apparition appears in front of you. Try talking with him, but he'll believe that you are the ghost, and not him. Take the washing bowl off the nearby table, and then take the mirror underneath it.
Use the mirror on Filliman (if he disappeared, click on the grotto again), and he'll finally believe that he is dead. Search the grotto to find his journal. Use the journal on him to give it to him. Ask if you can help him, and he'll ask for help becoming a nature spirit.
He needs "Something with faith, something from nature, and something of the spirit-to-become freely given".
Something from Nature
He'll give you a spell on papyrus, telling you to cast it in the swamp where there are dead logs. But first, you need to be blessed by Drezel. Head back up through the swamp, and speak to Drezel at Paterdomus.
Return to Mort Myre swamp, and look for one of the many rotting logs. Stand next to it, and cast the spell on the Druids' spell. The log will bloom with mory myre fungus; pick it.
Return to Filliman. Place the Mort Myre Fungus on the brown, western stone. Place the Used spell on the grey stone to the east, and you yourself stand on the orange stone to the south. Talk to Filliman, and tell him you think you solved the puzzle. He will cast a spell.
Search the grotto in the middle of the room, and speak to Filliman. He will finish the transformation by turning green. He will ask you to bring him a Silver sickle so that he may bless it so you can combat ghasts.
Talk to him again, and he will bless it. If you need to bless more sickles in the future, use it on the Wishing well in the grotto. He asks you to slay three ghasts. To do so, use the silver sickle, and right click while it is in your inventory (or operate it when it is weilded) and cast Bloom while standing next to rotting logs. This will take some prayer points.
When you have three Mort Myre Fungi in your inventory, click "Fill" on the Druid pouch that Filliman gave you to fill it. Now, when a ghast attacks you, it will take one of the fungi from the pouch rather than your food or life points.
Kill a ghast when they attack you and become visible; repeat for two more. You will get 30 prayer exp for killing each ghast. Once you kill three ghasts, return to Filliman. He will transform the grotto into an altar of nature.