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During the afternoon and early evening, British infantry are astonished to see many Christmas trees with candles and paper lanterns, on enemy parapets. There is much singing of carols, hymns and popular songs, and a gradual exchange of communication and even meetings in some areas. Many of these meetings are to arrange collection of bodies. In other places, firing continues.

This website cites a letter from Private H. Scrutton, Essex Regiment, published in the Norfolk Chronicle on 1 January, 1915:

As I told you before our trenches are only 30 or 40 yards away from the Germans. This led to an exciting incident the other day. Our fellows have been in the habit of shouting across to the enemy and we used to get answers from them. We were told to get into conversation with them and this is what happened:
From out trenches: “Good morning Fritz.” (No answer).
“Good morning Fritz.” (Still no answer).
“GOOD MORNING FRITZ.”
From German trenches: “Good morning.”
From our trench: “How are you?”
“All right.”
“Come over here, Fritz.”
“No. If I come I get shot.”
“No you won’t. Come on.”
“No fear.”
“Come and get some fags, Fritz.”
“No. You come half way and I meet you.”
“All right.”
One of our fellows thereupon stuffed his pocket with fags and got over the trench. The German got over his trench, and right enough they met half way and shook hands, Fitz taking the fags and giving cheese in exchange.”

Music:

The website continues:

The singing of hymns and carols between the trenches is perhaps one of the most atmospheric motifs of the Truce. Today it is the hymn Silent Night (Stille Nacht) most associated with the event but Allied soldiers rarely mention this hymn in their letters. Indeed, Rifleman Graham Williams said in his memoirs (1): ‘This was actually the first time I heard this carol, which was not then so popular in this country as it has since become’. He says O Come All Ye Faithful was the hymn which both sides started singing together. Other songs participating soldiers mention in their letters home include: Home Sweet Home, It’s A Long Way to Tipperary, The First Nowell, Old Folks at Home, Auld Lang Syne, While Shepherds Watched Their Flocks and O Tannenbaum. For a full list see http://www.christmastruce.co.uk/songs.html.