They either dropped a tree by the river or manhandled ( may have used a horse or mule) a close one across. Not a big ordeal with a couple of ropes and some leverage. The top of the log was probably flattened using an Adze, although you could have done it with an axe if you did it before you placed the log.

I actually helped my Grandfather build a couple of more elaborate timber bridges back before he died. He used a mule to help set the big cross river timbers. It was all supported on a rock and timber foundation. Lot of work, but kind of cool looking back on it.