There are many ways to obtain Super Magical Chest and legendaries. However, I'm assuming that you do not wish to pay a lot of money on this game, so I didn't include the option of purchasing Legendary King's chest. However, Legendary chests are a feasible option, so that's included below.
- Attempt to obtain the chest from battle.
You are guaranteed a Super Magical Chest, Legendary chest, and Epic chest every 500 chests. That means you have a 0.40% chance of obtaining a super magical/legendary chest from winning a battle. If you want to know EXACTLY when your Super Magical and/or Legendary chest will arrive, try royaleapi.com. Conditions: Arena 2 or above to get a Super Magical chest, Arena 7 or above for legendary chest - Purchase legendaries from the shop with gold
Occasionally, legendaries will appear in the shop, purchasable for 40 000 gold. This method is best if you want a specific legendary. Conditions: Arena 10 or above for legendaries to appear in the shop - Wait for the Legendary Chest Offer to appear in the shop
Occasionally, a Legendary chest will appear in the shop and can be purchased for 500 gems. This chest unlocks immediately and is limited to 1 per offer. (The offer will appear multiple times, however, usually every few weeks.) This chest guarantees 1 Legendary from any arena, but it's random, so it's best if you don't care what legendary you get. Conditions: Arena 4 or above (unverified) to receive chest offer - Try and get it from regular chests. Conditions: Arena 4 or above
Check out the chances of getting a legendary of any chest here: https://pixelcrux.com/Clash_Royale/Card_Chance/Calculator - Obtain Super Magical, Legendary, and Legendary King's chests from Quests
With the latest update (10/9/2017), chests are now obtainable as a Points reward for completing quests, and can reward ANY chest obtainable from battle (except Silver), as shown in the Quests screen.
Sources:
- http://clashroyale.wikia.com/wiki/Chests - card rarity, chest cycles, arena requirements for special chests
- I purchased 2 legendaries with gold.
- Personal experience - purchased legendary chest on Arenas 6, 8, 10, 11