The main objective in Pokémon is to catch Pokémon, which are randomly found in tall grass.
In order to catch Pokémon, you will need to use Poké Balls, there are many kinds of Poké Balls but the basics are Poké Ball, Great Ball, and Ultra Ball.
Wild Pokémon are weak at first but get progressively stronger as you move across the Hoen Map.
Some Pokémon are able of 'evolving', once evolved they will have a new look, higher stats and new moves.
You can not catch other trainer's Pokémon, only wild Pokémon.