The "Carp Route" is a popular method of fishing skillups in the game, as Moat Carp and Forest Carp is used in The Rivalry/The Competition quests and you will need 10,000 of them in order to obtain Lu Shang's Fishing Rod. Since it is possible to get fishing skill up to 56 by using Halcyon Rod + Insect Ball method, many fishermen go this route in hopes of fishing up over 10,000 Moat Carp by the time their skill will hit 56. This route is one of the slowest routes of getting the fishing skill, but one of the fastest routes to hitting the goal of Lu Shang's. Once this route is completed, most fishermen can focus on more profitable skill up fish without the worry of broken rods, as the Lu Shang's is very sturdy and can handle any type of fish.
Save all the Moat and Forest Carps you fished up and trade them to the NPC you opted to start the quest from.
It is strongly recommended to level Cooking skill into the mid 20s so you can make your own Insect Balls. Bait will really add up if bought from the AH or the Kazham vendors, however, you can make your own stacks for less than 400 gil per synth. Insect Balls take Earth Crystal, Distilled Water, Millioncorn, and Little Worm. Earth Crystals can be purchased for less than 1000 gil per stack, the other materials may be purchased from NPC vendors. Since consumable fishing bait only stacks to 12 and each synth yields 12 Insect Balls, some of the fishermen tend to bring the materials with them for crafting on the spot to save on inventory space.
Unless otherwise noted, always use Halcyon Rod and Insect Ball. The Halcyon Rod is the best rod when fishing for small fish, but there is one drawback: sandfish in Rabao will break it. Unless you have a low 70s alchemy skill to repair broken Halcyon Rods, it is preferred to fish in Rabao with Carbon Rods.
Level 1-11 - The early go
There are several spots to start, though Rabao is the best. If you head to Rabao, you will need to use a Carbon Fishing Rod instead of Halcyon, as Sandfish will break the Halcyon. Many fishermen will start in Windurst Woods or West Sarutabaruta (pond) instead of Rabao, partly due to the guild's location being nearby. Moat Carps cap at 11 fishing.
Level 11-20 - The Forest Carp
In order to safely do this, you will need to know how to get to the underground ponds in Yhoator Jungle. Goblins may wander by many of the ponds, which makes sneak fishing difficult at lower levels, but there are some exceptions: the dead ends in E-9 (on the way from the Teleport-Yhoat crystal to the third Yuhtunga Jungle zone) and F-8 (just south from the second Yuhtunga Jungle zone) only have non-aggro mobs. Your targets will be Moat Carps and Forest Carps. Over 75% of casts will hook a carp, of which about 1/3 will be Forest Carp. If your messages has "!!!", just release the fish as it is a mob or an Arrowwood Log. But from experience, mobs very rarely show up if Halcyon is used. Also don't bother trying to pull up a "bad feeling" fish, as it will just break your line. You may fish near Sea Serpent Grotto in Yuhtunga Jungle but the bite rate is not as good.
Level 20-33 - West Sarutabaruta
The Dark Bass is what you will skill up to Level 33 with, but you will catch a lot of Moat Carps in the process. If you fish to fatigue every day (200 fish), about 160-170 of the catches will be Moat Carps, and the rest will be Dark Bass. Mobs will rarely occur if you use Halcyon. I picked this location due to the proximity of the fishing guild.
Alternatives: Jugner Forest at lake may result in better skillups at first, but you will see considerably fewer moat carps than other places. The bite rate at La Thiene is horrible, so avoid that place.
Level 33-47 - Zeruhn Mines (River)
Do not use insect balls. Use little worms instead. Although Crayfish can be caught here, the stamina of those fish will be similar to items, so you can cancel them easily. All catches with !!! are Giant Catfish, which should be canceled as well. The prime skillups will be Black Eels, which will bite on little worms but not insect balls. Moat and Tricolored Carp can be caught here as well, but both have a similar stamina depletion rate. About 25% of the catches will be Black Eels, the rest split almost evenly between the two carps. The major drawback is that Black Eels can break the Halcyon, but only when you get a "terrible" feeling message, which should be canceled.
Level 38-50 - Rabao
Level 50-56 - Windurst Waters
The skillup targets will be Gold Carps, but there are still Moat Carps to pull up. If you head to Jugner, make sure to cancel all !!! that pops up, as they are mobs or arrowwood logs that will break your rods.
By the time you hit 56 fishing skill, you should have most if not all the 10,000 carps that you need. If you need more, continue fishing for Moat Carps in Rabao until the quest is finished, then move on to the next phase of fishing skill ups.