Enter the Goblin Cave east of the fishing guild (teleport to the Ardougne lodestone and run north). Once inside, head north, then east where you find Petra trapped in rock. Right-click and select "Search".
Go to Ardougne and speak to Wizard Cromperty. (south from the lodestone, then east to the house with the blue floor) (4•2)
Whilst you are in Ardougne, pick up five pigeon cages south of the north-western bank.
Go to the Feldip Hills and talk to Rantz. (Yanille lodestone > run south and past Gu'Tanoth on the east side > follow the shore east to Rantz) (1•3•4)
Go west until you see Gnormadium Avlafrim and a gnome glider. Talk to him (4•1) and search each landing light for a gem, cut it, and put it back in the landing lights (from west to east is sapphire, opal, red topaz, jade). If you crush one talk to him again to buy a replacement (4). Talk to the gnome again. (4)