When you find the pet you are interested in, make sure you make a reasonable offer to the seller within the app. Once the seller agrees to your price this will prompt them to send you a "Payment request" for the agreed amount.
To make an offer all you need to do is:
Open a direct chat between you and the seller for the listing of the pet that you would like to bring home.
Tap on the "Make offer" button.
Choose a reasonable price (don't offer anything less that 80% of the asking price) this will better your chances of getting the pet.
You may even choose to edit your offer after you've made an initial offer.
Wait for the seller to accept your offer (you can follow up with them).
Ask them to send you a payment request on the app after they accept your offer so that you can complete the payment process within the app.