It is a bit of a learning curve. You can set the game on easy until you get the hang of it.
You are likely out of cards so fast because you are burning them. If you look through your card deck, you will notice icons on some of them that show the card burning some only burn on either the top or bottom, making the other side safe to play. These are often your better plays but you then lose that whole card for the rest of the scenario. save the burn actions for either the end or when you really need them. It gets easier after the first few scenarios. Also, it is recommended to play as a group of 3.

It sounds like you're burning too many cards.
Each card has four options; a default attack, a default move, a top action and a bottom action. Most of the time, whether you pick a default action or a regular action, the card will be discarded after the turn and you can get it back when you rest. Some top actions or bottom actions will burn the card. A burned card doesn't go to the discard pile. Instead it is considered used up for the rest of the scenario unless you have some ability for recovering burned cards. Cards can also be burned to avoid damage but this should generally be done as rarely as possible.
If you're using all your biggest, strongest abilities to clear the first two rooms, you'll run out fast. Instead, set up combinations with your more durable abilities and save the best stuff for when it will have the greatest effect.

The tinker has a 12 card hand so that's 6 rounds in the first cycle. Are you burning cards to avoid damage? I recommend your priority scale look like this:

Avoid getting hit -> deal damage -> everything else

The main ways to avoid getting hit are to position yourself so monsters can't reach you and use crowd control abilities like stun/disarm/immobilize. Some of this will depend on you learning monster programming (which the digital version doesn't really explain). Often you can accomplish this by picking a late initiative so monsters move close but can't hit you, and then you go and can hit them.