Pick your lengths of wood prior to building your fence, as the length and width will matter in how you lay the logs in the zigzag pattern. Overly large pieces may be split down to size with an axe. Stand with your feet apart with a log between your legs and swing the axe so that the blade sinks into the center of the log -- or as close as you can get -- and work your way down the length until you have split it in two.
Start your fence by laying the base logs in position. Begin at the bottom and work your way up. Lay out your base layer of logs in the angle of zigzag you like, then overlap the edges, leaving at least six inches at each end beyond the section of overlap.
Lay the second layer on top of the first, ensuring that the rails overlap by at least six inches. Alternate the thick and thin ends of logs if you need to adjust the overall "levelness" of the structure. Continue stacking each additional row on top of each other, using the initial layer as your guideline for the angle of zigzag and placement of logs.
Tie off each overlapping section of logs with wire ties for additional support. Wrap the wire around the overlapping sections and then loop the loose ends of the wire together tightly and twist them several times to tie them off.