Dragon Slayer

Requirements

A hammer
3 Planks (just regular, not oak - found at Barbarian Outpost due north of the Agility course, Graveyard of Shadows, or at the spawn point in Port Khazard)
90 Steel nails (members can obtain these from the Sawmill operator northeast of Varrock, and they can be smithed by all players using 6 steel bars at 34 Smithing)
An unfired bowl (requires 8 Crafting to make)
A Wizard's mind bomb (bought in the Rising Sun Inn for 3 coins)
A lobster pot
A piece of silk (can be stolen from the Ardougne silk stall (requires 20 Thieving), or bought from Thessalia for 30 coins, or from the Al Kharid silk stall for 3 coins, 2 coins if you talk to him and refuse his first offer)
The anti-dragon shield (obtainable from the Duke of Lumbridge after talking to the Guildmaster for second time)
2,000 coins
A Ranged/Magic weapon, an air rune, and a law rune (if your Magic level is 33 or higher) or 10,000 coins

Once you've gotten the Maze key from the Guildmaster head to Rimmington.
Enter Melzar's Maze.
Kill the small zombie rat with a long tail to get the key and enter the northmost door and climb up the ladder.
Kill the ghost wearing hood, a tube top, and no cape to get the key and enter the second door from the north on the eastern wall and climb up the ladder.
Kill the skeleton with the round shield to get the key and enter the westmost door on the southern wall and climb down the ladder 3 times.
Kill the zombies to get the key and enter the blue door.
Kill Melzar the Mad to get the key and enter the purple (magenta) door.
Kill the lesser demon to get the key and enter the green door.
Open and search the chest to receive a map piece.

Go to the jail in Port Sarim.
Either kill Wormbrain and telegrab the map piece or pay him 10,000 coins for it.

Talk to Oracle on Ice Mountain. Make sure you have talked to the Guildmaster about where the Thalzar's map piece is.
Enter the Dwarven mine and use silk, lobster pot, unfired bowl and USE wizard's mind bomb on the magic door at the northeast side of the mine.
Enter the magic door, open and search the chest to receive a map piece.

Grab 3 wood planks, 90 steel nails, and a hammer out of the bank.
Talk to Klarense in the southern docks of Port Sarim by the Void Outpost boat and pay him 2,000 gp.
Go on board, climb down the ladder and repair the hole 3 times.
Talk to Ned in Draynor with the map in your inventory.

Return to the boat in Port Sarim you previously repaired and talk to Captain Ned.
Climb on top of the volcano and enter the hole.
Head south and kill Elvarg. Flinch Elvarg in the southeast corner of her cave for a long, but safe fight.

Quest Complete!