A red Gyarados is just a shiny Gyarados. There is no specialty, so just check your Pokédex to see where Gyarados is and start fishing. The chance of a shiny is just too small to look for it purposely. Or you can activate the code for shiny Pokémon and capture Gyarados.
A red gyarados is a shiny gyarados (however, the Pokemon Company did not call them shiny untill the Unova Region). You can find it wherever you can find a normal gyarados, but your chances to find it are very slim.
You can catch red Gyarados anywhere because red Gyarados are only shiny but are extremely rare.
The Red Gyarados is a standard pokémon you'll encounter in HeartGold/SoulSilver, but not in Diamond. In Diamond it's a 'normal' shiny pokémon, which means that you need to be very lucky to catch one. You can find Gyarados at many places in Diamond, but the chance of getting a shiny pokémon is 0.0122%.
train it
Easy! Just trade the red gyarados from soulsilver to diamond.
Its anywhere you can catch normal Gyarados in the wild, but its like a 1/8112 chance of finding one. Also, red gyarados' evolve from shiny magikarp at level 20 just like a normal magikarp
To get a red Gyarados in Pokemon LeafGreen you first need to catch a shiny Magikarp. This shiny Magikarp will be able to evolve into a red Gyarados. This is due to the red Gyarados simply being the shiny color of Gyarados.
In Pokemon Crystal version, you catch it at the Lake of Rage.
I think it is on the lake near the legendar pokemon. I not that sure.
Catch a shiny magikarp and evolve it.
GYARADOS
A red gyarados is just a shiny gyarados, it will still take time to accomplish.