It's a lot more involved than the Munchkin game you bought to the cottage, but having played that has helped greatly. You still have the same race/class cards, weapons, armour etc, as well as treasures and monsters, but the game progresses somewhat along these lines:

Each person has three move tokens. Draw a DxM card, keep or play.

Decide which room to move into, either an established room or into the dark. If into the dark draw a new room and place it down. Doorways can cost between 0-3 moves to change between rooms.

New (dark) rooms always contain a monster. Battle monster. If you win, monster leaves. You can spend another move if you have one, looting the room, or moving on. If not, run away or take a hit (lose a health token or two) and perhaps die.

You get a D10 power that rests on a die roll for extra powers.

When your go is over, the monsters move. Monsters, like munchkins, can have modifiers, and some have movement rules. A die roll decides the monster movements and sometimes they can form mobs. Monsters can move through many rooms on their travels. If you get chased down by a mob of monsters it can be a bit 'eek'.

Battle deals and trades still apply.

A bit too much to explain, really. We shall have to set up a game with you and MrsA.