In my opinion card awakening is the most deceptive feature of the game. (Maybe this opinion isn't correct, but it's obvious to me who has awakened, and what they have awakened, and so it maybe a misinterpretation on my part.)
First thing to note is that awakening a card uses mana, and mana is about the rarest substance in the game. It can not be purchased. It is typically acquired as a reward from events, and for reading the news feeds that N3twork posts in-game. It takes a long time to acquire mana due to these limited sources of acquisition.
Second thing is: Just because there is a banner showing that an awakening is possible doesn't mean you should. This banner, like the game, is trying to get you to spend your valuable resources, because ultimately LGOH is all about the dollar. The more time, money, and effort you spend, the more money N3twork makes.
Irrespective of what the Starter Guide says awakening is more often, than not, a detriment to your deck of cards, and the team that the awakened cards were on. The guide was released when the game was released, and maybe awakening (as talked about in the guide) made sense then, but now with the events, and their free card drops, giving away more, and more, powerful cards the awakening information from the guide should be reconsidered.
Please consider the following points:
Now let me tell you why awakening doesn't make sense to me:
A team consists of 5 cards, and each normal card has a power of 5 for a total of 25 power. If you have two support cards that adds a total of 10 power to your team. The other 15 power comes from the other cards on your team, and they could be cards acquired in previous events, or from random draws. So if you use one of the support cards to awaken the other support card the awakened card has a power of 6 now (awakening adds 20 percent to a card, and it takes 5 awakening to double the power of a card, 20% of 5 is 1, and 5+1+1+1+1+1=10). Once the two support cards have been combined through an awakening the total power of the team is now 21, but the team also has an open slot for a new card. If you can not replace the lost awakened card with a card of equal or better value, then your team has less power than before.
A completed event team has two support cards, one nuke card (GvG), one ultra rare card, and one collection card. This combination, with the event relic(s), gives you the maximum team power.
When Should You Awaken a Card
Here are the typical, logical awakening scenarios
Don't waste mana: