Cut logs at least 6 inches in diameter and long enough to reach across the cabin floor. Choose a rot-resistant wood, such as cedar, locust or Osage orange, and select logs that are all approximately the same diameter. Use an axe to cut them to length, or, if you're using power tools, a chainsaw. Cut enough that you can space them 2 to 4 feet apart across the floor.
Hew the top of each log flat with a broad-axe or adz so you have a roughly flat surface, 2 to 3 inches wide.
Lay the logs directly on the ground across the cabin floor, placing one against each wall and spacing the rest the same distance apart, which should be between 2 and 4 feet. These are the sleepers that will support the puncheons.
Cut logs that are 8 or more inches in diameter and the same length as the distance from the center of one sleeper to the next. Use a chainsaw or cross-cut saw so the ends will be flat. Choose a durable wood that will split easily, such as oak or cedar.
Insert an iron wedge in the end of one of the logs, toward the edge, and pound it partially in with a sledgehammer or maul. As a crack opens, add a second wedge along the top of the log and pound it in also until the first wedge loosens. Insert the first wedge beyond the second and continue until the crack extends the full length of the log and it splits in half. If the split starts to run crooked across the end of the log, insert an additional wedge in the end to keep it straight.
Trim off any remaining fibers of wood between the two log halves with an axe so they separate fully. Use a broad-axe or adz to smooth the flat face of each half. This will be the surface of the floor.
Snap a chalk line along one side of the flat face. Measure the same distance across on both ends with a tape measure, and snap another chalk line. Hew the sides to these lines with an axe or broad-axe to make the top surface square.
Chalk a line on each end, parallel to the flat surface and about 2 inches below it. Turn the logs flat-side-down and hew each end at an angle with an axe, so it tapers to meet the line. This completes one puncheon.
Split and finish enough similar puncheons to cover the entire floor, if they're placed side-by-side across the sleepers.
Place the puncheons across the sleepers, flat side up. If they don't fit closely side-by-side, trim off any protrusions with an axe or hatchet. Drill two holes at the end of each puncheon down into the sleeper, using a 1-inch auger, spacing the holes 1 to 2 inches from the sides of the puncheon.
Split out and trim 1-inch-diameter pegs from a piece of wood slightly longer than the holes are deep. Use a hatchet to make the pegs. Pound them into the holes with a mallet and trim off the tops level with the floor, using a hatchet or saw.