Dragon Slayer/Quick guide

Beginning

 * Talk to Guildmaster in Champions' Guild. (Chat 2)
 * Talk to Oziach in Edgeville. (Chat 1, 1, 1, 1)
 * Talk to Guildmaster in Champions' Guild. (Chat 2, 1, 1, 1, 2, 3, 4, 3) Make sure you have the maze key.

Map pieces
Melzar's map piece
 * Map pieces must be obtained in order.
 * After obtaining all 3, combine them by using them to each other.
 * Enter Melzar's Maze in Rimmington.
 * 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 door.
 * Kill the lesser demon to get the key and enter the green door.
 * Open and search the chest to receive a map piece.

Thalzar's map piece

 * Talk to Oracle on the Ice mountain. (Chat 1)
 * Enter the Dwarven mine and use silk, lobster pot, unfired bowl and wizard's mind bomb on the magic door.
 * Enter the magic door, open and search the chest to receive a map piece.

Lozar's 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.

Obtaining a boat

 * Talk to Klarense in the docks of Port Sarim and pay him 2000 gp. (Chat 4, 1)
 * Go on board and climb down the ladder and repair the hole 3 times.
 * Talk to Ned in Draynor with the map in your inventory. (Chat 1)

The fight

 * Talk to Captain Ned in the boat you bought. (Chat 1)
 * Climb on top of the volcano and enter the hole.
 * Head south and kill Elvarg.

Finishing up

 * Talk to Oziach in Edgeville.
 * Quest complete!