The words are by Robert Burns (1759-1796), Scotland's national poet, who built them on an older Scottish song. "Auld lang syne" is Scots for "old long since", roughly "days gone by". The song asks whether old friends should be forgotten, and answers by raising "a cup o' kindness" to them.
The tune is a traditional Scottish melody, and the custom of singing it to see the old year out began in Scotland, at Hogmanay, before it spread around the world. In Scotland people join hands in a circle and, for the last verse, cross their arms to take the hands of the people on either side.
This transcription: Traditional Scottish tune with words by Robert Burns, the melody as it is sung today: in G major; left hand by GOONS Studio.
Transcribed by GOONS Studio from the original work, which is in the public domain.
On guitar: Auld Lang Syne guitar chords and lyrics, with a guitar that strums along.