Banned things tend to vary from people's rules, but these are the general things that are banned competitively:
-OHKO moves like Fissure, Sheer cold, or Guillotine.
-Evasion/Accuracy changing moves like Double Team or Sand Attack. However, Abilities that boost evasion such as Snow Cloak and Sand Veil are still allowed.
-Pokemon in an inappropriate place. (If you are in a Neverused tier, you would not be allowed to use Arceus. You can check online, or make your own rules for tiers. Some people use them, and others tailor them to meet their desires.)
-Freeze/Sleep Clause-no two pokemon are allowed to be frozen or put two sleep at the same time. You can however, have one pokemon asleep and another frozen.
-Species Clause-You can't have more than one of the same pokemon. Imagine putting 6 Arceus on a team...
Item Clause-You can't have two of the same item. (This one is rarely enforced)
There might be other rules people set, but with these, you should be fine.