White flag

. Tie a shirt to a stick and wave it around.
Or, the ever-more-common:
"Hey, Yank/Reb, don't shoot!"
Afterwards, an officer would cross the lines with the flag and whatever message he was carrying. He would be taken to the nearest command post, and his message forwarded up the chain of command to the general commanding. While the truce officer swapped cigars and newspapers with the enemy soldiers watching him, the general would then write a response that would filter back down to the truce officer. The officer would then take the message and, waving his flag, make his way back across the lines.
At this time, of course, there was the famous camaraderie between pickets that never went away however much officers on both sides tried, so it was pretty easy to start truces, whether formal or informal.