In order to grow your steemmonsters deck you have to invest quite a bit of steem. Several hunder dollars worth of it. But there is another way. Within the game you are able to finish a daily quest which can gain you some small to moderate rewards. And sometimes even a worthwile legendary card you can use for your battles.
This is my way, so I decided to work on the daily quest. To beat it you have to win 5 battles (non consecutive) with a certain type of deck. You can choose between life, earth, fire, death, and water. The amount of battles you have to perform depends quite a bit on the type of deck you have to use for that day. I find that the death deck makes for easy victories, while the water deck can take a long time.
One of my battles of today was;
https://steemmonsters.com?battle=d5607274ddc8cdc93e7ed7764570a5b19d00f5a3&ref=thunderbluff