What am I supposed to do in Tazaar's house?

You're looking for a key, somewhere in the house.  I would recommend doing
whatever you can, and you'll eventually stumble on it.

Start by making yourself a nice pot of tea.

You can do that by heating up some water in the kettle on the back wall.

Pour the bottle of water into the kettle (F).

Then use the matches on the kettle to light it (F).

Look!  There's a key on the wall!  But before you can get it, you'll have to
find a way to keep from the goblins reaching into all that steam.

The best way to do that is just to turn off the flame underneath the kettle.