The in-text citation for a personal communication like a conversation includes more detail than citations for other sources. It contains the author's first initial and last name, the words "personal communication" (without the quotation marks) and the specific date of the event in month-day-year order. Place a comma after the last name, after "communication" and between the day and year in the date. A typical citation might look like this: (J. Smith, personal communication, March 31, 2013).
Generally, sources cited in the text of your paper need to have an entry on the References page at the end of the paper that gives the remainder of the bibliographical information about the source. Personal communications differ, however. Since your reader cannot go find your conversation and get more information about it, the details in the in-text citation must suffice. Personal communications and classical or sacred works (such as classic Greek texts or the Bible, for instance) are the only types of sources that do not need to appear on the References page.