How to get gold in Hearthstone

The Gamepedia article on Hearthstone card rarity explains gold cards this way:

Cards within the 4 basic rarities described above can have a chance of being obtained with a gold border with custom art animation. Gold cards do not appear frequently, and therefore add to the rarity of a card. Gold cards can also be crafted with Arcane Dust for ten/eight/four/two times the normal cost of the card (in order of rarity). Gold Cards are commonly compared with "foil" cards of other types of Trading Card Games (TCGs).

So basically, expert set gold cards drop randomly when opening packs or can be crafted. Additionally as indicated in this question and answer basic gold cards (which cannot be crafted) are earned by leveling heroes.

The community over at Hearthpwn has compiled a list of Leveling System Rewards (which is too long to enumerate here). Additionally the article on leveling in Hearthstone at Gamepedia provides insight.

Here are some interesting points to take away from the articles:

• Gold Cards are earned one at a time. Unlike the basic cards, which are earned in pairs.
• Heroes also earn golden versions of the basic set of Neutral cards.
• Class specific gold cards are earned between levels 11 - 49.
• Above level 50 golden basic neutral minion cards are awarded.
• To earn all gold neutral cards a player will have to level every hero to 60.
• Gold cards are earned at levels: 15, 20, 23, 26, 28, 30, 32, 34, 36, 40, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59 and 60.