So everyone starting out you will need to spend the $10 to get the spellbook to gain anything. This will give you starter cards that you can use, but can't sell. Then each day you will get a quest that you can do that will reward you one chest with 33% potion (that highers your chances for better cards), 33% card (a card from the current set of packs common-legendary), 33% DEC (DEC is game currency that you can turn into real money), and 1% to get a pack of 5 cards.
You have can only get to rank Bronze 3 before needing to buy cards or play for a couple months. The wins in Bronze 3 is usually less then 1 DEC per win. This will reward you with 5 chest same as the dailies. Then each common card is worth 10 power, each rare is worth 40 power, each epic is worth 200 power, each legendary is worth 1k power, and gold versions of the cards worth 50x as much (so a gold common is worth 500 power). So if you did your quest every day and then got bronze 3 you could get 20 chest in 15 days and 40 chest in a month. So that is an average of 13 cards. Those 13 cards will likely be around 160-400 power, since you are likely to get mostly commons which are only 10 power each. It will take you with little luck of cards around 6 months to even get bronze 2 rank for 1000 power. Then you will gain 2 extra chest and start gaining 1-4 DEC per win (with win streaks can get to the 4 DEC).
You can use your DEC to also buy/rent cards so it can be little quicker to get ranks as well if you do that. You can buy/rent cards on the www.peakmonsters.com/market webpage. Every card you rent you gain the power of that card till your rent is over.
The best option if your wanting to rank up/make money quickly is to spend more money on some decent cards and rent some. You can also try your luck on some packs. I have bought $20 worth of packs and only gained about 1500 power. Where my friend gained 4500 power from $20 as he got a gold card and a legendary.