All single-card purchases from the in-game Merchant are conducted with Gold. (Contrast this with Shadow Crystals, which are used to buy booster packs and starter decks).
You can gain Gold through winning games against the AI or against other players online. Gold can also be accumulated through selling cards back to the Merchant, where you receive half the Buy price of the card (i.e. a common card with a price of 100 Gold to buy, will get you 50 Gold when you sell it.)
A typical strategy for filling out a playset is to buy starter decks for Shadow Crystals and then selling the contents back to the Merchant for Gold, which can be spent on the needed cards. This tends to be more cost-efficient than buying Booster packs at the moment.