There are various ways to get legendary cards: 

• Playing in different game modes. If you score well in different game modes you will receive various rewards, and some of them may be Legendary cards.
• Exchange Quest. There is a possibility of earning a Legendary Card through the Card Exchange Quest, make sure to check it out regularly. For more information, check out the FAQ: Card Exchange Quest
• Collecting and exchanging Shards. You can exchange 100 Shard for a Legendary Card. For more information, check out the FAQ: Shards System
• Daily Deals. Sometimes, there will be legendary cards in the Daily Deal slots in the store.
• Legendary Chest. They can be found in the store, or through various offers.