First, make sure you have the furniture equipped. You equip furniture by selecting it in your inventory and pressing F. It'll show up in the furniture bar of your equipment page. Then, when in a dungeon, make sure you have that equipped piece of furniture active. The smallest circle in the bottom left corner of your HUD will show it if it's active (press E to cycle active furniture). Finally, hold down space and move the green floor marker to wherever you want to place the furniture. When you release space, the furniture will appear there.
We're planning on making the controls far more clear to the user in the coming update, and I'll make sure to relay your suggestion about a weapon shop to the designers.