Assembling your killer team of Pokémon is one of the fun things about Pokémon. To do that, you'll need to obtain some Pokémon first. Initially you'll be given a starter Pokémon to, um, get you started. But the rest is on you and this is where Poke Balls and catching Pokémon becomes key.
Catching Pokémon is quite simple on paper. You just need to throw a Poke Ball at it and there's a chance the Pokémon will be caught (yay!) or it will break free (oh no!). To increase your odds, you should weaken the Pokémon down with your moves.
However, you don't want to drop the opposing Pokémon's HP down to 0, as it will faint and magically disappear, wasting your efforts (but providing experience). So try to watch their HP and use weak moves until their HP bar is very low or as low as it'll go before you think you'll faint it.
It also helps if you use a move that inflicts an ailment, such as Sleep or Paralyse , on the Pokémon, as this will increase the capture rate somewhat. Later, you can also use improved Poke Balls, like the Great Ball or Ultra Ball, when the critters become increasingly harder to snare.
An important thing to note: Only wild Pokémon can be caught, so don't bother trying to throw Poke Balls at other trainers' Pokémon!
After you've caught a Pokémon, you can use it for battle instantly. Although if you just caught it, you may need to heal it and train it before it becomes a viable party member. Do note that you can only have up to 6 Pokémon in your battle party at once.
If you catch any more Pokémon, they will be transported to a Pokémon box , which you can access from the PC inside any Pokémon Centre. You can also use the PC to move Pokémon from your party to your box(es) and vice versa--useful if you need to rejig your team.