When your hero dies, that's game over for you, so try to keep it safe.
You can attack enemies with your hero, but the safer option is to spawn monsters and let them do your fighting.
Monsters will form the backbone of your strategy to winning in combat – the clue is in the game title!
You can deploy monsters into combat during your own turn, but keep in mind that it's your hero who calls them forth, which means monsters can only be spawned on an empty space adjacent to your hero.
Use your spawned monsters to attack your enemies, but try to remember that whilst killing the enemy's hordes can be fun, you only have to kill their hero to win the battle.
Prior to starting a battle, you need to make a "deck". All of the various monsters and other items exist in card form, and it is your job to mix these cards together into a coherent deck.
This deck is shuffled at the start of combat and you then draw an initial "hand" of five cars. You also draw one card at the start of each of your turns*.
On your own turn, you can then play these cards onto the battlefield to spawn monsters etc.
(*Because going first can otherwise give a slight advantage, the starting player does not draw an additional card on their first turn.)
Every card has a Mojo cost required to play it. If you don't have enough Mojo at the time, you will not be able to do so. This cost can be seen as a purple number at the top/left of all card imagery.
You can earn Mojo various ways, but your Hero conveniently generates Mojo for you at the start of your turn – exactly how much depends upon the Hero you pick.