The Ooblet creatures are all over Badgetown, and they serve as your primary companion to follow you around. They do dance battles against other Ooblets they encounter in Oobets, but after defeating them, you do not have the chance the capture them to add them to your squad. Instead, you have the opportunity to acquire seed from the defeated Ooblet, and the seed is what you need to grow one yourself to add them to your squad.
When you want a seed of a particular Ooblet you need to approach them and offer them the type of vegetable or item they want. Afte you collect the items you need to offer them to the ooblets and then you and your team will engage theirs. At the end of the battle, the Ooblet you offered the items to will give you the option to take their seed or not. By doing so, you can return to your farm to plant it.
The Ooblet seed will grow like any plant in your garden. After a set amount of time and making sure the growing seed has water, it will sprout into the Ooblet you battled. You can choose to take them with you around town to battle other Ooblets, level them up, or have them remain on your farm.