How did Sam make his fireplace and bed in My Side of the Mountain?
Sam's bed is made "of ash slats and covered with deerskin". His fireplace, which is "about knee high", is made of clay and stones, and has "a chimney that leads the smoke out through a knothole".
Sam binds strong branches together to make his bed frame, and weaves a platform that will serve to hold his mattress out of ash slats. The ash slats "work very well, and are quite springy and comfortable". At first, Sam piles hemlock boughs on the ash slats to make a soft sleeping surface, but hopes to eventually have a deer hide to take their place. Sam's bed fits neatly into a space on the right-hand side of his hollowed-out tree.
Making a fireplace is a much more difficult undertaking for Sam; it takes him three days to get it right "so that it (doesn't) smoke (him) out of the tree like a bee". He makes the chimney out of clay, but finds that it sags because it is "too heavy to hold itself up". Sam works some dry grasses into the clay to strengthen it to the point to where it will hold its own weight. He then whittles a hole through one of the tree's knotholes to allow smoke from the fireplace to escape, and builds the chimney down from this, but finds that when the clay dries, it shrinks and pulls away from the tree, allowing the smoke to pour back into the tree's interior. Sam seals the leak with pine pitch, which works for awhile, but then he finds that the funnel over the fire bed cracks, and must find a way to fix that. After trying a number of methods to no avail, Sam finally discovers a large, flat stone to hold up the funnel, and the fireplace is at last usable.
In a scary turn of events, Sam notices that his pet bird Frightful becomes lethargic before the cozy warmth of the fireplace, and realizes that the fire is consuming all the oxygen in the tree. Understanding that he must provide more ventilation for their safety, he cuts several more holes in the tree, and eventually finds that the air circulates enough for them to use the fireplace safely.