I'll just list some basic rules that I know of a regular Nuzlocke:
- You are allowed to catch one Pokemon from each route / place / etc and swap it for the egg.
- If any of the Pokemon you have faint, then you would have to put it back in a PC Box labeled "dead" or release it.
Here are some clauses that can help or challenge you:
- Gym Leader Clause: If you get swept by a gym leader, your Pokemon are not dead and you can still use it.
- Same Pokemon Clause: If you get a same Pokemon from an egg, you'll have to release it or put it in a PC Box labeled "dead".
- Gifts Clause: You can get "gift" Pokemon and use it on your team. It can or cannot be considered the first Pokemon encountered in the city.
Note that some of the names are just made up by me :P , but those are some of the common clauses.
Good luck on your Nuzlocke! And make sure you always stick to the rules.