First up is this simple method, from Jean-Marie at 1st Facebook Scout Group:

"Let's suppose I do not have a rope long enough, but just a stick/small rope, even smaller than the half of the long one. I set it at one end, perpendicular to the pole, and mark the point (usually, leaving a scout standing there). I do the same thing at the other end of the pole BUT ON THE OTHER SIDE. The imaginary line between the 2 scouts cuts the pole in its middle. Thus, when the Scouts see me on the line between themselves an their opposite pal while I walk along the length of the pole, I have found the middle.That's it ! The longer the pole, the longer the stick, the more accurate."

These three methods are all variations on direct measurement - measuring with a rope and folding the rope in half, using a tape measure and halving it, or pacing out with a shoe, a shorter stick, a ruler or any other item.

Finally, the centre of balance / centre of gravity for a pole can be found by a few methods, but this is a simple and quick one courtesy of Jean-Marie at 1st Facebook - put a short section of round pole underneath the pole, then push the pole forward or backwards until it balances like a see-saw. If you have a pole without much taper, this will get you close to the midpoint of the pole too, but if the pole tapers a lot, you'll be better off using one of hte methods above to find the exact middle.

*drawn on iPad Mini using Paper app and Just-Mobile AluPen*