Gold cards are precious and rare, so they can only be traded on exceptional occasions.
When the Golden Trade event is live, a number of gold cards will become open and available for trading for a limited time. You can always find the golden trade event in the card section of the game and tapping on the button will show if the event is live.
Any extra cards can be sent to friends or offered on our trading groups, and unowned cards can be requested in the same manner. Make sure you have your notifications enabled so you never miss one of these events!