A key part of delivering humor in a speech, or even in standup, is to sell the setup.  By 'Selling', I mean the process in which the speaker accomplish the following objectives:

1. Provide the necessary background information

2. Mislead the audience into one direction

3. Hide any traces of impending punchline

A big component of a humorous story is the surprise ending of the punchline.   A secondary component is the logic of the punchline.  It has to make sense, although not in the way that the audience intended.  Any missing information, the audience will say, 'what?  I don't get it'.  And if the audience can guess the ending, then the reaction is "Oh, I saw that coming a hundred miles away."

This article will provide a case study to illustrate this idea.  It is from the speech "Youthful Mistake".  You must watch the video first (click on read more), and then read the comments in the text for analysis of the final part in the conclusion.

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Analysis

The doctor told me, that for the next 2 months, I had to be gentle with my hands, or else it will cause more damage, requiring more surgery. 

(This  provides the background information:  I need 2 months to heal, I can't do any hardwork.  Vital information for the punch line.)

So, I spent that time reflecting on my youthful mistake.   I have to find something good from this tragedy. 

(This sets the audience up for the surprise.  They are expecting that something good comes out of the experience) 

So I learned to be more patient and to think before I act. 

(This continues to lead the audience on.  The trilogy:  I learned something good--patience--and something else good--to think before I act.  So the next item would also be good. )

A couple of weeks after my accident, I got a call from a female friend whom I was secretly in love with. 

(With the specific description of the situation, the audience now should expect that this will have a happy ending:  someone whom I like is going to sympathize with me, and might take care of me.  I have purposefully identified the thought that I want to place inside the audience.  Note, that I added it was only bit of time after my accident--I'm not healed yet.) 

(on the phone with her) "Yes, I’m doing fine, Thank you!" 

(to the audience)She called me to see how I'm doing!

(back on the phone) "Yes I have time this afternoon?"

(to the audience) She wants to see me! 

(on the phone) Yes, I'll be there in 10mins.

(So far the phone conversation continues to lead the audience to believe that I'm seeing her on a date)

Ladies and gentlemen.  Even after my tragic accident, and my damaged hands, my female friend still wanted me (LONG PAUSE)

(At this point, I have setup the audience to finish the sentence for me:  my female friend still wanted me to be with her. But I finished the sentence with)

to move her furniture!

(This is the punchline!  I had the audience completely fooled!  The additional layer of humor was that I was stupid enough to risk my hand to help her move the furniture!)