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. <br>

 * Attempt to obtain the chest from battle. <br>
   *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 <br>
   *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 <br>
   *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**<br>
   *Check out the chances of getting a legendary of any chest here: https://pixelcrux.com/Clash_Royale/Card_Chance/Calculator*<br>
 * Obtain Super Magical, Legendary, and Legendary King's chests from Quests <br>
 *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: <br>

- http://clashroyale.wikia.com/wiki/Chests - card rarity, chest cycles, arena requirements for special chests <br>
- I purchased 2 legendaries with gold. <br>
- Personal experience - purchased legendary chest on Arenas 6, 8, 10, 11 <br>