Pokémon Rescue Team Mystery Dungeon DX is a little different from many other games in the Pokémon universe. You don't play as a trainer and instead play as a Pokémon. This makes catching Pokémon in the game a lot different, as you can't throw PokéBalls.
The first thing you need to do is unlock the ability to recruit other Pokémon. To do this, play through the game until you reach the third Mt. Steel dungeon. Once you have defeated Skarmory, you will be able to recruit other Pokémon.
How to recruit Pokémon
Now, you won't be able to recruit them right away, as you need to provide your team members with a place they can live when they're not our rescue of other Pokémon. You will need camps where they can stay, and different types of Pokémon need camps that match their type. To get your first camps, go visit Wigglytuff in town, and they'll give you three camps for free. As long as there is room in the camp and it matches the type of Pokémon, you can now start recruiting the Pokémon you find in the dungeons.
When you defeat a Pokémon and your team leader delivers the final blow, there is a chance it will join your team. If this happens, the Pokémon will join your team, effectively giving you an extra member. You must then exit the dungeon safely, and then you will have the option to recruit them permanently if you wish.
When you see a Pokemon you want, be sure to land the final blow with your team leader. You can change the team leader by pressing the + button on your Joycon.
