You have to go through a castle and retrieve a tail (probably renamed), then go to the small islands to the west of the castle. You will be rewarded with the class change.

The castle is in the central-north area of the map. A little to the east side. It's like Ohio if the World of FF was the US, I think.

edit: hey just looked at your other post and noticed you are from ohio, lol! Ironic.

The castle is like a dungeon with a bunch of hard enemies, but the Cave in the Islands doesn't have any enemies. It is inhabited by dragons, with Bahamut as their king. I think this is the same as the NES version, I haven't played through DoS's FF1, but I've played the NES version.