Obtaining the Trident of the Red Rooster is one of the most difficult and arduous feats in the entire game. It takes considerable time and effort as well as careful planning, spread throughout the game.
Khelevaster
First, the player must Save Khelevaster, which requires an Amulet of Life Saving - a very rare item, especially as early in the game as it is required.
Possible tactics for retrieving an AoLS at this point of the game include wishing (as Rings of Djinni Summoning are more frequent than amulets of live saving, remember to bless before using!). Common methods of obtaining a wish include Gremlin Bombing, extensive grave digging or sipping from a Pool and being lucky enough to gain a Wish. A large amount of pools can be found in Darkforge. Saving Khelavaster grants, among other things, a reward of six scrolls of chaos resistance, which will be extremely helpful in the latter parts of the quest. The lawful boost for saving him may be one to look out for.
Sharad-Waador
Then, after saving Khelevaster, the player must successfully navigate to the bottom of the Caverns of Chaos to reach the Unreal Cave sidebranch, and Kill Srraxxarrakex as requested by Sharad-Waador. This is quite a task even for higher leveled players, as it requires travelling through the the dangerous Blue Dragon Caves and killing a very powerful Wyrm.
Filk
Assuming that task is accomplished, the player must then achieve character level 45 (assuming they aren't already at that level or above), and visit the Assassin's Guild and receive the Kill Filk quest from the Assassin Prince.
Depending on how prepared you are, this is either extremely easy or very hard. Filk can be found on the level of the Infinite Dungeon that matches your first kill (If your first kill was a Large Bat and you have killed 60 large bats, he will be found on level 60 of the dungeon).
Thus, if you have planned in advance and made an extremely rare monster your first kill - for example, a Beggar, which can only be found in Lawenilothehl - then Filk can be easily reached. If, however, your first kill was something like a Kobold or an Orc, it will likely be a long trek.
Note that no special message is given when you get to the level Filk can be found on, so if you are unsure of your first kill it will be even harder to accomplish this quest as you will have to thoroughly check each and every dungeon level to see if he is on that level. If you leave the level he is on, but come back later, you can NOT find him there again.
There are reports of players finding Filk randomly wandering the wilderness after a player leaves his level in the ID, however this has not at this point been confirmed. If found, he reportedly will attempt to join your party.
Once you have found him - be it in the wilderness or the Infinite Dungeon - you have to kill him, and that is quite a task in and of itself. He is extremely fast, the fastest monster in the game, and also has the highest DV in the game. Because of these two features, it is recommended that you use some form of unavoidable spell, for example Improved Fireball to quickly kill him. (Any ball spell, Burning Hands, crystal of fire, offensive alchemy will do.)
Assuming you manage to kill him, you can then go to the Mad Minstrel and receive a reward - the location of the Scintillating Cave.
The Emperor Moloch
The bottom level of the Scintillating Cave, a dangerous place in itself, is the home of the Emperor Moloch, an extremely slow, but also extremely strong adversary. Unlike Filk, he has almost zero DV, while having the highest PV in the game. As such, it is recommended you use attacks that either bypass PV entirely (phase dagger or a weapon of penetration) or deal enough damage to get past it (such as blessed arrows or quarrels of demon slaying).
If you kill the Emperor Moloch, he will drop the Crumpled Scroll, which can then be taken to Khelevaster, who by now has returned to the small town of Terinyo. If a lawful or neutral player gives him the crumpled scroll, he will summon for them the legendary Trident. Don't do it while chaotic!