Golden cards are special, rarer versions of cards.
The difference between a card's normal version and its golden version is only looks it does not have any added stat bonuses only nicer looking with unique animations. Golden cards are just for showing off your card collection. Golden cards do not allow you to use 2 regular versions of the same card totaling four in your deck 2 max.
Each card is available as a golden card.
How to get
You have a small chance to get a golden version of the card you would normally get whether it be through card packs crafting or leveling your Hero level.
A golden version of each basic card can be obtained by leveling a specific class of hero to a certain level. So if you want to start collecting golden cards your best bet is to level all of your Hero classes as high as you can.
Golden basic cards are not allowed to be disenchanted or crafted.
Golden cards from the expert set can be obtained through card packs, or through crafting. Each card found in a card pack has a chance to be automatically upgraded to its golden version. Obviously with how expensive crafting is the chances of getting a golden card is very small, but that should not stop you from trying.