The Common English 'How Do You Do' (16th c. or earlier) appeared in print as 'howdy' in England in the 19th c. (origin much earlier?), but as noted by Azizi, it was and is common vernacular in the U. S. South and West.

The greeting shout "How Do You Do, Everybody, How Do You Do," posted by Azizi, had its origin in the 1920s as the theme song of Billy Jones and Ernie Hare, "The Happiness Boys", very popular on early radio, 1929-1939.

It is possible, however, that the melody goes back to some of the 19th c. Billy Barlow routines.