This is the full list of clauses that are used in Competitive Battling.
These first six clauses are standard rules that, unless stated, will and shall be used in all battles that you will come across:
Evasion clause -You and your opponent can not use evasion increasing moves like double team and minimize. This clause also includes Accuracy reducing moves as well, but usually are not specified as switching negates the accuracy reduction.
Legit/legal clause - All Pokemon have to be legit. None of the Pokemon can have illegal movesets, 999 in all stats, 255 EVs in all stats, or have been caught in places that they normally wouldn't have been caught at. An example of an illegal moveset would be would be a Magnezone with Flamethrower or Salamance with Ice Beam.
OHKO clause - You and your opponent can not use moves that causes instant one-hit knockouts. Some examples would be sheer cold, fissure, and guillotine.
Sleep clause - Only one Pokemon can be to sleep (on your side of the field) at a time. The only time your opponent can use another sleep move is when your Pokemon either wakes up or faints, then your opponent can use a sleep move again. The move Rest does not count toward sleep clause, so if your opponent were to put a Pokemon asleep because of Rest, you can still use a sleep inducing move on your opponent.
Species clause - You and your opponent can not use more then one of the same Pokemon. This means that you or your opponent can not use two Infernapes or Garchomps or two of the same Pokemon in general.
Uber clause - You and your opponent cannot use ubers in a battle.
Those are all of the standard rules.
Now for rules that usually aren't used in standard battles but you might be asked to flow them:
Baton Pass Clause - You and your opponent can not use the move Baton pass. This is to avoid straight out sweepage at the beginning of a battle because of the passed stats.
Focus Sash/Choice Item Clause - You and your opponent can not use more than one focus sash and choice items (choice scarf, choice specs, choice band) in a battle.
Freeze Clause - You and your opponent can not use moves that can freeze you after a Pokemon has already been frozen. You will have to wait for the frozen Pokemon to faint or thaw out before you can use another move that can possibly cause a freeze. Even though that it is a rare occurrence to freeze your opponent's Pokemon, not many people feel like losing due to a freeze. A few moves that cause freeze would be Ice Punch, Ice Beam, Blizzard, and Powder Snow.
Hidden Power Clause - You and your opponent can not use the move hidden power. This was most likely created because some people think that using hidden power on a Pokemon is unfair and that the user hacked to get the right Hidden Power.
Luck items Clause - You and your opponent can not use Items that rely on luck to be activated. Some examples are focus band, bright powder, and quick claw.
Perfect IV Clause - You and your opponent can not use Pokemon that have perfect IVs in all stats, since it is so rare to get Pokemon with 31 IVs in all stats. Many would consider it hacking if you have a Pokemon with 31 IVs in all stats.
Poison Clause - You and your opponent can not use moves that can or are specifically made to poison. Toxic, Smog, Sludge Bomb, and Sludge are all good examples of moves that cause poison.
Sandstorm Clause - You and your opponent can not use the move sandstorm or have Pokemon that can create a sandstorm. Only two Pokemon can create sandstorms by ability. These Pokemon are Tyranitar and Hippowdon.
Self-KO clause - You and your opponent can not use moves that KO yourself when it is your last Pokemon vs your opponent's last Pokemon. This is to avoid draws in battle. Some examples are Self-Destruct and Explosion. Destiny Bond does fall under this clause if it works.
Shiny Clause - You and your opponent can not use a team that has a lot of Pokemon shiny. People may use this as many people who hack usually make their Pokemon shiny as well.
Site Tier Clause - You and your opponent can not use any other tier list other than this site's tier list. This is mostly to avoid confusion on what Pokemon is where in another site's tier list. Something like Alakazam is considered (At the current time) BL on this site, but on most other sites, it is considered OU. So, if you ask for a BL battle on this site, but you know another site's tier list but you do not know this site's tier list, and Alakazam is considered OU on the site's tier list that you know, and your opponent brings an Alakazam into the battle, then ask why they brought Alakazam.
Skarmbliss/SkarmCressBliss Clause - You and your opponent can not use Skarmory and Blissey (and Cresselia, if you are using SkarmCressBliss Clause) on the same team. You can only have one of them on your team.
Switching Clause - You and your opponent can not switch out a Pokemon in battle. This excludes moves that force switching, like Roar and Whirlwind
UBERS/OU/BL/UU/NU Battle - You can request what kind of tier you want to play in. If you just want OUs in the battle, then post somewhere in your post or your title that you want an OU battle. If you want a BL battle, then post in your post or in your title that you want a BL battle. You do the same thing for the lower tiers as well. If you want to combine a few tiers together like BL/UU/NU, then post in your post or in you title that you want a BL and lower battle.
Now that you know what each clause means and which clauses are standard for all battles and which clauses are optional that you can add to any battle, go out there and battle with your (hopefully) new knowledge about the clauses.