You'll receive a number of quests related to pets. And the system will send a Sunflower Fledgling to every novice player.
Capture will fail if the pet escaped the net. If a pet is ensnared by the net, then it will appear in your bag.
In Pockie Ninja, you can only capture a pet by searching the wilderness and encountering one randomly.
You should launch an attack by means of casting a net.