Gold vanity skins are obtained by collecting a certain number of duplicate cards. The amount of duplicate cards required will vary from character to character but once a gold vanity skin has been equipped to a character a unique effect will become unlocked for them.
Regardless if a card is equipped in a current deck or stored in an inventory there is only a limited amount of each card you can possess. Any additional cards you may have picked up through rewards or card packs that grant duplicate cards will automatically go to be disenchanted for inks and count towards unlocking a gold vanity skin.
You can always check your progress in obtaining gold vanity skins by going to the 'Cards' icon at the main menu and selecting from any of the available Houses or faction to review current card inventory. When you then choose a character the progress towards obtaining the gold vanity skin will be displayed with the option to 'Pick a Costume'.