NOTE: Despite the quest level, this quest shouldn't be attempted without a high-level party, or at least a level 77 Spectral Dancer.
1. Port from Goddard to the entrance of the Forge of the Gods. Go down the ramp. Cross the bridge. Take the first left (don't go right) then after that take every right turn, and stick to the right. You'll soon find him in a safe spot. Once you find him, he has a lot to say.
2. Klein tells you to bring him a Vacualite from Blacksmith Hilda in Goddard. With it he can create a Floating Stone for you to get through the Hall of Flames.
3. In Goddard, Blacksmith Hilda tells you to bring her some Vacualite ore. She tells you to hunt in the Garden of Wild Beasts and kill Kookaburra, Bandersnatch, and Grendel. Bring back 50 Vacualite ore. These mobs are 1/2 HP.
4. Once you have the 50 quest items, return to Blacksmith Hilda. She'll make the Vacualite. Now you can return with it to Klein in Forge of the Gods.
5. Talk to Klein again and he turns the Vacualite the Floating Stone. After that, you can port to the small hallway above the lava flow that you can see behind Klein, and the Floating Stone disappears. Just a tip: after you get the Floating Stone from Klein, talk to him and pick up the quest again.