Instructions
Play through the game until you are in the dungeon. Many quests are available in the dungeon as it goes down for dozens of levels.
Fight your way through the dungeon until you are down between the 10th and 25th floors. These are the most common areas to find the Trident.
Fight enemies and check weapon racks on any of these floors. Enemies are in no short supply in the dungeon, but the Trident is not a particularly common drop. Fight enemies until one drops a Trident. If you happen to see an enemy wielding a Trident on the lower floors, kill it -- it has a higher chance of dropping a Trident.
Find Getts the Traveler in the dungeon. He appears at random and always has a randomized inventory. If he has a Trident, he will sell it to you for 520 gold.