To add your card to Google Pay, go to the "Finances" section visible at the main screen in the application, select the card that you want to add to Google Pay, scroll down and you will see "Add to Google Pay" button. You will be asked for your card data and accept the Terms and Conditions for the use of the Google Pay service.
You can also add a card directly from the Google Pay app. Download the application, follow the instructions on the screen and accept the card issuer's terms and conditions. You will receive an SMS code to enter to verify your details. The card will appear as a payment method, set it as your default card for contactless payments.