The Two Big rules are:
1). If a pokemon faints, its considered dead, and you cant use it anymore
2). You can only catch the first pokemon you see per region (Route, Cave, Town, etc) nothing else. The only exception is if you see one that youve already caught.

And the third rule most people do is that you have to give a nickname to all your pokeymans

So I can only catch one pokemon in each route? Like say I was a Dunsparce and I go to Route Seven (Just making shit up,) and I get a Ferret, I cant go back for a Dunsparce?

Like, you go to route 7, if you see a dunsparce first, you can only catch THAT dunsparce. If you kill it or run, no second chances, you've lost your one pokemon for the route. And if you catch it, thats it, you can run into wild pokemon still, but you cant catch it. But that only applies to that route. That rule is confusing, so Id say go with your best judgement, considering Nuzlocke is basically built on house rules.

I can't understand what you just said, I'm sorry. But let me try to clear it up, you're being a bad ass trainer and enter route 7. You got yourself your Totodile named Percy and boom, wild pokémon. Fuck it's a Rattata. Now you gotta decide: Do I catch it, kill it, or run. If you run or kill it, then too bad, you can't ever catch a Pokémon on Route 7. Not even another Rattata. That specific one or bust.