Welcome to the challenge rules page!
The most basic Nuzlocke rules, as they were first introduced, are as follows:
1) Any Pokémon that faints is considered dead, and must be released or put in the Pokémon Storage System permanently.
2) The player may only catch the first Pokémon encountered in each area, and none else. If the first Pokémon encountered faints or flees, there are no second chances. If there's a static encounter in the area, the player is allowed to capture them despite already capturing a Pokémon in that area. Shiny Pokémon also do not apply to this rule.
3) The general consensus is that players must also nickname all of their Pokémon, for the sake of forming stronger emotional bonds.
4) The general consensus is that a black out/white out is considered to be "game over", even if there are Pokémon left in the PC.
5) Strongly implied, though not explicitly mentioned in the comic, is the stipulation that the player can use only Pokémon they have captured themselves, meaning traded Pokémon, mystery gifts, etc., are prohibited. Trading and retrading the same Pokémon (for the purpose of evolving a Graveler, for example) is something of a gray area, and may fall under optional rules.
This story will be about a trainer trying to remember his past after losing a big battle. As he completes the island challenge and collects the Z-Crystals it will allow him to regain his memories. Because the routes are so big in my story the routes will be split into quadrants to allow for the story flow better. The main character will be able talk to his pokemon thanks to Tapu KoKo.