The most common way to obtain these materials is to run the special Challenge Dungeons, where they have a chance to drop when you clear the Dungeon (higher difficulties offer a better chance for a drop).<br>
The Awakening Materials may also sometimes be obtained through Special Campaigns or Gachas.
Something to keep in mind is that there is a Special Mission for getting a Card into an "Awakening State" for the first time. (eg. the Card is at Max Lv and Max Skill Lv and can be Awakened.) <br>
The first Card you get into this State will trigger the Mission's Completion and you can claim an Awakening Material Package as a Reward, giving you all the materials you need to Awaken your first Card.
With recent updates to the Challenge Dungeons, you can now earn Points when you beat them. <br>
Added in the 2.5.8 update, certain Cards can now be "further Awakened" allowing them to be upgraded even further, increasing their base stats and enhancing their Skills. <br> Essentially, this acts as a "Second Awakening" or a "Super Awakening" (referred to as S.Awakening on Card Pages).
In order for a Card to Awaken even further, the following conditions must be met:
*The card must be capable of further Awakening. (Thus, they must already be Awakened.)
*The card must be at Max Level.
*You must have the required Evolution Materials. These are the same Materials used to Awaken them in the first place.
*The card's new Cost cannot run over your Total Deck Cost limit. (If you have the above conditions fulfilled, but the Card still can't Awaken, check your various Decks; especially your Duel Match Decks.)
Of course, there are a few quirks with how further Awakening works.
*After achieving further Awakening, the card will remain at Level 120 and retain its previous Skill Level.
*The card's maximum stats also increase by ~10% from before.
*Some cards will have their Skills changed as well as their Cost and Orb Slots increased.
*Card rarity is unchanged (e.g. If a card was GOD before, it remains GOD-rarity after Awakening.)