In order to make purchases, you will need an active Google Play account for Androids or an active iTunes account for iOS Devices. You will either need to redeem a gift card with monetary value to these accounts or connect them to a credit card.
 
Once your account has been set up, simply tap the Buy button located at the top of your game screen. This will bring up a selection of chip packages currently available for purchase—follow the instructions from there to make the purchase.
 
Setting up Payment for Google Play account:
 
Setting up Payment for iTunes account: