Catching is when a trainer encounters wild Pokémon and battles to lower their health enough to be captured using Poké Balls. Poké Balls are consumable items used to store a Pokémon. Some Pokémon may unlock avatars upon capture. Trainers can only encounter Common and Rare spawns at the beginning and would require Ribbons to encounter higher rarity spawns. Contrary to popular belief, cutting out potential spawns by intentionally not obtaining Ribbons does not increase your chances of getting a specific Pokémon, and in actuality, lowers your chances of encountering higher rarities the fewer Ribbons you have. Mystic variant's scare mechanic does not prevent the trainer from capturing.
Unlike the Main Series, status conditions do not affect catching, nor can they be inflicted in wild battles. It is as simple as lowering their health points to the required threshold for specific Poké Balls.
Catch Rate & Threshold
Keep in mind, reducing their health to the requirements only grants you the possibility to capture and would not guarantee your catch.