Card Trades themselves are set up by players over different platforms such as Facebook Messenger.
To send a card, open your card collections by pressing on the card icon found at the bottom left corner of the screen. Then, tap on the set containing the card you want to send. Tap on the card you wish to send and then on the Send button which will open up a list of friends.
Please note that you can only send a card if you have more than 1, and Gold Cards can only be traded during special events.