Most cartridge-based Pokémon tournaments have no restrictions on using pseudo legendaries. If you're talking about VGC or Battle Spot (the formats you can play on cartridge), pseudo legendaries aren't banned in Regulations G and H and have rarely been in the past.
If you're talking about unofficial tournaments like the ones you play on Pokémon Showdown, the pseudos are categorised into tiers just like every other Pokémon and cannot be used in a tier lower than their own. For example, this means you can't use Dragonite in UU. If you're playing on cartridge, there's no need to worry about these restrictions.
