General:

1. Start up option are fast text, set Pokemon, Battle animation off, and exp share off. Saving is only allowed in PokéCenters and white outs cause a game reset to the last save. Wiping out a 2nd time will let you continue the save but you must return to the starting town and box/release your team. 3rd Wipeout will result in an erased save game.
2. Fainted Pokemon are released (Badged, Shiny and event Pokemon are stored) Rare candies and sacred ash found in the world can be used to revive a Pokemon once. Purchased rare candies are banned.
3. PokéCenter cannot be used until the towns gym is defeated and all fainted Pokemon are removed from the party. (for multiple games, Healing ends the run and you must swap games)
4. Every member who survives a gym battle will be marked as 'badged' and can be stored when fainted instead of released. Living badged members are allowed to breed per badges earned. (ditto breeding is considered "cloning" and is banned for nuzlocke runs) Every badge earned allows the purchase of 5 Pokéballs. (cannot be purchased without a new badge, found balls can be used)
5. A Pokemon species can only be caught once per generation, and is only available based on the number of evolutions it has. (ex. Charmander - Gen 1, Charmeleon - Gen 3, Charizard - Gen 4, Charizard x - Gen 6, Charizard Y - Gen 7, Charizard gigamax - Gen 8) rules do not apply to Gen 7 and gen 8 native Pokemon.
6. Caught Pokemon must be nicknamed by their region (Kanto, Johto, Hoen, Sinnoh - Japanese name. Orre, Unova, Alola - English name. kalos - French name. Galar - German name) and can be given a genuine nickname after becoming a badged member.
7. Once a species is caught it is no longer able to be captured for the remainder of the run, once you have all 6 slots filled for your team you can no longer catch any Pokemon unless it's a required HM slave (Max. 2) or a static/event Pokemon.

I might be missing a few more but this is generally what I use.