The Pokémart is the place to be if you want to capture mobs to place in your worlds. Inside it you can buy Pokéballs for most mob types. Make sure to check the tooltips for more information about which mob types a ball can catch, the catch percentage and the price.
Using the Pokéballs is quite simple: you aim at the mob and right-click to throw. They behave a lot like Ender Pearls when throwing, but you might want to pick up some cheap balls to practice first.
