Beating Normal and Hard Mode
Beating normal mode is one of the first barriers in the game to overcome. While these guides I've listed below are written specifically with hard mode in mind, if you read these you will not only win your games, but you'll progress in a way that prepares you for hard mode as well. If you apply hard mode strategies to normal, very quickly normal mode will become easy mode.
The most important parts
I reccomend reading at least these four guides about game mechanics if you want to start winning every normal mode match you play.
Reading mythic roles will also help.
Beating Hell Mode
To find out how to advance from hard mode to hell mode, check out the guide How to Beat Hell Mode.
There are also unique bosses in this mode that can attack your board, killing or debuffing your units. You can see the full list of these bosses here.
Below I've embedded a demonstation of the physical damage hell mode strategy.