How do I earn new cards in Mortal Kombat X?

In Mortal Kombat X there are quite a few ways to unlock new cards. The first and easiest way to get new cards are to buy card packs from the store which will give you a random card of the rarity you selected. Also note that there are three rarities of cards that you can obtain, Bronze, Silver, and Gold and they increase in power as you go from Bronze to Silver then Gold with Gold being the strongest cards you can get. There are cards you can buy in the store that aren't in packs but I would recommend not buying these as they cost a lot more than the random card packs.

The second more difficult way to get cards is to participate in events, in Mortal Kombat X there are events hosted every month or so where you can obtain rare event cards that are unique to the event and won't be purchasable in the store after the event. These are usually long strings of battles with some sort of gimmick imposed on you, such as bronze only cards or what not.

The third way of getting cards is through the "story mode" after you complete certain towers you may receive a card when you complete the tower. However they usually give you bronze cards that are honestly not that great so I would mostly focus on buying card packs and getting your ranks boosted with higher tier cards faster.

Hope that helps.