1) If a Pokemon faints, it’s dead and can no longer be used in any capacity. You can release it or you can deposit it into a box marked “Dead” and never take it out, but it can’t be used in battle, nor can it be used for HMs. Redos are NOT allowed; if a Pokemon faints, you can't simply retry the battle (well you can but the spirit of Nuzlocke will frown upon you).

2) You can only catch the first Pokemon you run into in any route/area, and you only get one chance. If you accidentally faint it or run out of Pokeballs, then that’s too bad for you. What makes up an area is debatable at times; a good rule of thumb is that if a new location indicator pops up that is different from where you just were, it’s a new area.

3) You must nickname all of your Pokemon. These Pokemon are your lifelong friends, they will fight for you until they die! You must bond with them, and the first step to creating a bond is to nickname.

Some other rules include:
-Repeats. Some people are willing to catch 5 <insert overly common early-game Pokemon here>, others aren’t. If you want variety in your team, feel free to modify the “first Pokemon you see” rule so that if it’s a Pokemon you already have you can ignore it. On the other hand, if you want to go hardcore with your army of <insert overly common early-game Pokemon here>, you can go right ahead.

-Item use. Usually either at any time, outside of battle only, in battle only, or not at all. Choose whatever you feel is best for you. Some people even allow Revives in specific occurrences, though that arguably goes against the spirit of the challenge.

-Pokemon Center use. Unlimited use is most common, but some people like to make the challenge more difficult by either limiting the amount of times they can use the Pokemon Center in each town or by making it cost more money each time (you can simulate this by buying items equal to the imposed cost then trashing them). If you really feel like a challenge, you can ban Pokemon Center (and PC) healing entirely as well.

-Legendaries. Usually not allowed to be used (though if you want to you can), but sometimes people like to go the extra mile and force themselves to beat the legendaries.

-Level limit. Being 20 levels higher than everything trivializes the challenge, so most players will usually avoid being any higher than a major foe’s strongest Pokemon. In a similar vein, usually people don’t just use one Pokemon for the same reason (plus you’re just asking for some horrible luck to completely screw you over by doing that).

-Gift Pokemon. Usually they simply count as the Pokemon you get for that area, such as Eevee for Celadon/Goldenrod. However, some people disallow them entirely.

-Switch and set. Generally people play on set for the increased challenge (plus it’s more conductive to a story), but if you prefer to make it easier you can always play on switch (where you get to choose to switch out whenever you KO a Pokemon, whereas on set it’s like competitive battling).