Q. How do I cite a speech?

APA

You do not cite the speech itself. Find an authoritative location where the speech is and cite that. For example, if you were reading the speech in a book, simply cite the book. If you read the speech on a website, cite the website.

For example, if you’ve found Dr. King’s speech in a book of great speeches, your reference might be as follows. 

Smith, J. (Ed.). (2009). Well said! Great speeches in American history. 
   Washington, DC: E & K Publishing.

The in-text citation would include the surname of the author or editor of the source document and the year of publication.  For example, your sentence might look like this: 

Dr. King declared, “I have a dream that one day this nation will rise up and live out the true meaning of its creed” (Smith, 2009).

MLA

• Provide the speaker's name,
• Title of the speech or lecture, using quotation marks. If there isn't a title of the speech, describe what kind of speech it is without quotation marks (For example: Commencement Address, Lecture, Keynote Address, etc.)
• If applicable - Organization/Club/Sponsor,
• The location, including the building and the city,
• Day, month, year.

Example:
Simpleton, Joe. "Nationalization of Government." Preservation of Democracy Society. Freedom Hall, Knoxville. 10 January 2009.