How to get the Excalibur Weapon in FF4
The quest to get Excalibur starts in the Land of Summons with the Rat Tail you receive from one of the treasure chests. If you missed this on your first trip through the dungeon I recommend you use my FF4 Chapter 9 Walkthrough <Add Link> for help finding it.
Once you obtain the Rat Tail you'll be able to complete the next part of the quest once you get the Drill attachment for the Falcon and you can travel freely between the Overworld and Underworld. When you've made it this far you'll want to first return to where you left the Enterprise and the Hovercraft.
For those of you that have forgotten, we left both of these by Eblan Castle. A screen shot of their locations (assuming you did not move either of them) are shown below.
Back in control of the Enterprise, you'll want to pick up the Hovercraft which you'll then carry with you over to to the town of Mythril which is nearby the Adamant Grotto. If you go to Fabul Castle first, you'll find the town of Mythril directly south of it.
In my screen shot below you'll see the town of Mythril to the north and the Adamant Grotto we're heading to in the south. All that you have to do inside of the Adamant Grotto is speak with the kid inside and hand him the Rat Tail you got earlier. In return you'll get the Admantite ore which you'll need to bring to a smith in the Underworld.
After you get the Adamantite Ore you'll want to head to the Kokkol's Smithy which is located in the southeastern portion of the Underworld. When you come down the hole into the Underworld just head directly south and you'll find Kokkol's Smithy.
On the second floor of the building you'll find one of the dwarfs sleeping in a bed. Hand him the Admantite Ore and he'll take your Sword of Legend too, both of which will be used to create the Excalibur. We can't get this sword just yet, first you'll need to ride the Lunar Whale to the moon.
Note: The Lunar Whale is unable to enter the Underworld, once you ride it back to the planet you'll need to board the Falcon and ride that down to the Underworld