First: How it's calculated.
Power or Collection Power is the sum of the Burn Rate of all the PLAYABLE cards in your collection- so , cards rented by you count but cards on the market or delegated out don't.
The Burn Rate of cards is set by this handy, dandy chart:
As you can see, 3 things influence the Burn value of a card:
Rarity, Expansion, and Foil with Gold cards being worth 50x what regular cards are.
How to get Collection Power, cheap
Renting. Renting cards is the cheapest way to add power to your collection.
I've found that these are the cheapest places to rent power:
Gold, Rare, Untamed/Dice/Reward cards: 1,200 Power per DEC/Day (@1.5 DEC/day)
Gold, Common, Alpha/Promo cards: 1,000 Power per DEC/Day (@1.5 DEC/day)
Gold, Legendary, Alpha/Promo cards: 1,000 Power per DEC/Day (@150 DEC/day)
Gold, Epic, Untamed/Dice/Reward cards: 1,000 Power per DEC/day (@10 DEC/day)
Prices can change and, obviously, you may have to pay a little more for USABLE cards, which may be worth it- since you will get the 10% bonus when you win a game using a gold card.
Always check the Price/BCX, as combined cards multiply their Burn Rate and may give you the best value when renting for POWER!