We know from stories and songs written down at this time that these palaces were built mainly of big wooden beams. They had rammed earth walls, like the buildings of the Shang Dynasty. They had courtyards. Archaeology tells us that some of these buildings had clay roof tiles.
The songs also tell us that rich people's houses already looked a lot the way rich people's houses looked in later China, with walls around them and courtyards and more private areas for the women in the back.
The Zhou emperors made laws about how fancy your house could be. Only the emperors were allowed to have artists carve their pillars and paint them red. Only the very richest families could paint their pillars black. People who were not so rich painted their pillars yellow.
But most people were too poor to have any pillars at all in their house, and they just had rammed earth walls, whitewashed or plastered to keep them clean, with a firepit in the center, just like in the Shang dynasty.