Select your logs before starting the fence. You can either purchase the wood directly from a lumberyard, or you can look for wood in the wild so long as you own the property, as it is illegal to take wood off of federal land or other people's property. Logs should be around 10 feet in length, and around three or four inches in diameter, although personal preference may dictate otherwise depending on the size you want. Split larger logs down their length with an axe.
Lay out the perimeter of your fence with a selection of logs to use as a reference point for the rest of the fence. The exact angle of your zigzag pattern will vary depending on your preferences, but the goal is to have the ends of each rail overlapping the next piece in the fence by at least 4 inches. Lay your entire first row of logs before you begin working on the rest of the fence so you can establish your area.
Work your way up from the bottom and stack each log so that the logs overlap on the ends, using your initial pattern of logs as a reference. Adjust the overall straightness of the horizontal fence rows by alternating thin and thick ends of logs as necessary where they overlap at each cross section. If you want, tie off each overlapping section with wire for additional stability.
Add vertical supports for your fence if it goes above waist-height. Cut the end of an appropriate-sized log to a point with your axe, similar to a sharpened pencil, or pick a log that already has a somewhat-pointed end. Lean it vertically within the outermost cross-section of logs so that it is tucked in between the end of each section where the four inches of exposed logs cross like an X, and use the flat end of the axe to drive it into the ground. Tie your sections to the post with wires for additional support.