From the sheet music at National Library of Australia:

HOW DO YOU DO
Words and music by Phil Fleming, Charlie Harrison & Cal DeVoll.
Sydney : D. Davis & Co., c1924.
Chicago : Ted Browne Music Co. Inc., c1924.

1. How do you do, ev'rybody? How do you do?
How do you do, ev'rybody? How are you?
When the skies are kinda grey
And you're feeling just that way,
Ain't it great to hear folks say,
"How do you do?"

CHORUS 1: How do you do? (How do you do?)
How do you do? (How do you do?)
How do you doodle, doodle, doodle, doodle do?
So from Maine up to Alaska,
Here is what we want to ask ya:
How do you doodle, doodle, doodle, doodle do?

2. How do you do, old timers? How do you do?
How do you do, old timers? How are you?
You remember way back when
Girls were girls and men were men.
It's so different now from then.
How do you do?

CHORUS 2: How do you do? (How do you do?)
How do you do? (How do you do?)
How do you doodle, doodle, doodle, doodle do?
Now even grandmas bob their hair,
Smoke cigarettes, and learn to swear.
How do you doodle, doodle, doodle, doodle do?

EXTRA VERSES AND CHORUSES:

3. How do you do, Rudolph Valentino, etc.
Tho' they've never heard you speak,
All the girls go every week
Just to see their darling sheik.
How do you do?

How do you do, etc.
Now, it's not your face that's fair;
It's the way you comb your hair.
How do you do, etc.

4. How do you do, Mister Rooster, etc.
Can you tell me, Missus Hen,
When will eggs come down again?
You haven't laid eggs since Lord knows when.
How do you do?

How do you do, etc.
Though you think you're getting by,
You're going to be a chicken pie.
How do you do, etc.

5. How do you do, society folks, etc.
Every year you have a craze
That just lasts a few short days,
But here's one I'll bet that stays:
How do you do?

How do you do, etc.
So forget your old Mah Jong
And learn this crazy little song:
How do you do, etc.

6. How do you do, radio friends, etc.
Now you've heard us sing a lot
But you liked this "Tommy rot."
Some was good and some was not.
How do you do?

How do you do, etc.
Just who wrote it, we've forgotten,
But it's written rotten, rotten.
How do you do, etc.

7. How do you do, Mister Darrow, etc.
How do you do, Tennessee, etc.
"Monkey Trials" we cannot see,
But we read of them with glee,
And we care not what it be.
How do you do?

How do you do, etc.
We have not the slightest fear
For we all have brothers here.
How do you do, etc.

7. How do you do, old Broadway, etc.
I have been to all your shows,
Sat down in the baldhead rows.
The girls are pretty, I suppose.
How do you do?

How do you do, etc.
But I felt so out of place,
I couldn't look them in the face.
How do you do, etc.

8. A: How do you do, etc.
B: How do you do, etc.
A: Now, I hope you'll like this song.
B: Well, I hope it's not too long.
Am I right?
A: No, you are wrong.
How do you do?

Both: How do you do? How do you do?
How do you doodle, etc.
B: Well, I'm glad you're nearly done.
A: Why, I've only just begun.
Both: How do you doodle, etc.

9. How do you do, Andy Gump, etc.
How is Chester? How is Min?
How's the whiskers on your chin,
Growing out our growing in?
How do you do?

How do you do, etc.
In the papers you can bet,
You're the biggest laugh we get.
How do you do, etc.