These are the basic battling rules used for competitive battles on Wi-Fi and Shoddy Battle.
No Ubers
This means that the Pokemon on this list are banned, except from designated uber battles. In addition, Rotom formes are banned in Wi-Fi battles.
Sleep Clause
Only one Pokemon on each team can be asleep at a time. Once that Pokemon wakes up or faints, it or another Pokemon can be put to sleep again. Pokemon who have fallen asleep due to Rest are not counted in this limit.
Species Clause
Each Pokemon must be of a different species. Different Pokedex number means it's a different species.
Evasion Clause
The moves Double Team and Minimize are banned.
OHKO Clause
The moves Fissure, Sheer Cold, Horn Drill, and Guillotine are banned.
No Illegal Hacks
No Pokemon can be hacked to have moves it usually does not have or higher stats than it should have.