It happened along the Western Front which is nearly 500 miles long and I know that not every area was peaceful. But for the places that were far apart and had truces were they unrelated incidents that happened by themselves or did it somehow spread from one place?
Yes, it was very much an unofficial and local affair, arranged spontaneously between units occupying trenches opposite each other. It did not stretch the whole length of the front (in fact it was confined to exchanges between British and German troops, but the best estimate is that there may have been truces along about two-thirds of the length of the British line), nor did it take place at any one time; there are accounts of unofficial truces, and attempts to arrange more, from Christmas Eve to as late as New Year. When word of such arrangements made it back to headquarters, attempts were made to prevent such fraternisation – and in the winter of 1915 specific orders were issued to prevent any repetition.
The first overtures were made by the Germans. One account, written by a British private, Frederick Heath, explained the origins of the truce in his sector as follows:
"All down our line of trenches there came to our ears a greeting unique in war: ‘English soldier, English soldier, a merry Christmas, a merry Christmas!’"
Then–as Heath wrote in a letter home–the voices added:
"‘Come out, English soldier; come out here to us.’ For some little time we were cautious, and did not even answer. Officers, fearing treachery, ordered the men to be silent. But up and down our line one heard the men answering that Christmas greeting from the enemy. How could we resist wishing each other a Merry Christmas, even though we might be at each other’s throats immediately afterwards? So we kept up a running conversation with the Germans, all the while our hands ready on our rifles. Blood and peace, enmity and fraternity—war’s most amazing paradox. The night wore on to dawn—a night made easier by songs from the German trenches, the pipings of piccolos and from our broad lines laughter and Christmas carols. Not a shot was fired.'"
It is very noticeable that the units likely to agree such truces were not elite formations. The Prussians, on the German side, and Guards units, on the British, did not participate, and the war continued as usual in their sectors. Saxon units (considered to be especially easy going) and to a lesser extent Bavarians were most likely to be involved on the German side.
On consequence of the sporadic and partial nature of the truce was that there was no single football match between the British and the German troops – perhaps the most famous part of the truce story as it is usually told. Rather, there were at least three or four different games arranged, of varying levels of sophistication. One game was won by the men of a Scottish regiment, 4-1; another saw the Germans victorious, 3-2.
There is an extensive literature on the truce. I wrote about it in more detail here, if you'd like to learn more.