The process is started by "planting" foundation sticks in the mud, and then building the superstructure on that. The superstructure is built using sticks, bark (from deciduous trees), rocks, mud, grass, leaves, masses of plants, and anything else available, just like a dam.   Once the dome is completed, the beavers will approach from below the water line and dig/chew an entry tunnel and two chambers. The entry tunnels to the lodge are built so that the only access is below the water line.  The floor of the first chamber is a few inches above the water level. This chamber is used as an eating area and to dry off after coming out of the water, making it kind of a combination dining room and mud room. The floor of the second chamber is above the first, and is used for sleeping and caring for kits. The floor is covered with a layer of shredded wood or vegetation. This stacked chamber design reduces the weight of the walls and helps prevent cave-ins.   A lodge is usually occupied by only a single-family group of up to 18 beavers. This family group would include an adult pair, that year's kits, and young from the previous year. 
Young beavers take on adult duties such as building and maintaining the lodge and dams in their second summer.  They also sometimes act as babysitters for the new litter of kits.  A beaver lodge is used year after year, and beavers will add material to their lodge every year, even if repairs are not necessary. This can lead to some lodges becoming quite large.  During winter, beavers do not hibernate. They will stay active in their lodges, sealed off from the outside world by the frozen layer of winter ice on the river. Beavers will store enough food under the ice to last until next spring.  During winter, you can see moist warm air rising from the vent hole in the top of the dome, like smoke from a chimney. This is a sign of how much warmer the temperature on the inside is, than outside.  The damp walls of the lodge will freeze, adding to the installation and also making the lodge impervious to predators.