Dwarf Cannon Quest
This quest is required to used the dwarf cannon. The cannon is very important for most bosses, and this quest is fairly fast. Therefore, it's definitely worth it to do this quest.
The only items needed for this quest are 3 law runes, 3 water runes, and 3 air runes. (Shown below)
First, teleport to Ardougne and follow the path shown below. At the first red star, activate the Ardougne lodestone, which will be used later on in this quest.
The world map showing the path taken after teleporting to Ardounge. See the image below for an explanation of each star.
Activating the Ardounge lodestone, shown on the world map above as the lower of the two red stars.
After reaching the second red star, you will find a dwarf named Captain Lawgof. Talk to Lawgof, and he will tell you that the railing around his base needs to be fixed. He will give you 6 railing parts, and a hammer.
In order to fix the railings, you must inspect them. Since each railing looks the same, it is best to investigate each railing in a methodical pattern. Moving clockwise around the fence, inspect each railing (one per square).
Inspect each railing (shown above). The railings are shown on the world map below.
After all of the railings are fixed, talk to Captain Lawgof again. He will give you a cannon mould, and tell you to take it to Nulodion in Falador. Teleport to Falador, and follow the path to Nulodion on the world map shown below.
When you arrive at the red star, talk to Nulodion to receive his notes.
After receiving Nulodion's notes, use the home teleport spell to go back to the Ardounge lodestone.
From here, follow the path shown on the world map below.
When you arrive at the red star, talk to Captain Lawgof to complete the quest.