I have used a dome type of shelter, based on the traditional sweat lodge. I use river willow that's about 1"-1 1/2" in diameter at the base. I suppose that you could use small diameter sapplings, but for this shelter, it takes about 30 lengths to construct it correctly. Again, you could use more or less depending on the length of the saplings and the diameter of the hut.
I start by gathering the willow or saplings. Then make a circle in the area where I want to put it. I place a stake in the center of where the lodge/hut will stand, tie a 3-4' piece of line to it and tie a stick to the other end. Then I walk it in a circle, marking out the circle. Then I devide it into 16 even spaces, making a mark in each place. I sharpen the base of 16 willows and stick them into the ground on the marks that I just made and start bending the willow, tying each vertical to the vertical on the other side of the circle from it. Crossing them as I work my way around. Then I start at the base and start tying in the horizontals, four rows. Once it's all tied together, I cut out the door and start covering. I use a tarp and ponchos to cover it so that it's more or less waterproof. It's a tough and very sturdy shelter that will last for many years. All you would have to do is recover it when you want to use it. If you use mud and other natural materials and leave a smoke hole, you might be able to get away with a small fire using a dakota hole, but my choice would be to build a fire away from the hut.