JFK is often quoted with the following statement:
"Today, we need a nation of Minutemen, citizens who are not only
prepared to take arms, but citizens who regard the preservation of
freedom as the basic purpose of their daily lives and who are willing
to consciously work and sacrifice for that freedom."

I would like to know what the context of the speech was and the full
text of the speech?  Who did he give the speech to?  Where?  When? 
And what was the full text?  Thank you.

http://www.keepandbeararms.com/downloads/GunFacts_v3.2.pdf

See page 73. The quote appears to be from "Guns" magazine, April 1960,
Page 4 "Know your Lawmakers." [Cited at footnote 317]

However, the NRA has two references to the "nation of minutemen" quote
which suggest it was included in an "address" before March 7, 1961.
Their "invitation" to accept a life membership, and the White House
response, are reproduced here:

http://www.nracentral.com/nra-jfk-life-membership.php
http://www.nracentral.com/jfk-nra-life-membership.php

Notice that even the NRA letter is somewhat vague in its time
reference, though, which may suggest that they had just picked up on
the quote in the magazine article (and decided to capitalize on it)
... and the magazine reference seems to be one of the "scorecard" type
questions interest groups send out to find a legislator's views on
certain issues. Note, e.g., on that same page in the first reference
above that Hubert Humphrey also seems to have responded to the
question (see footnote 318), also in 1960.

It still is possible that all these items resulted from an actual
speech, but I don't see any reference to it in my quick search, even
of the Kennedy Library website.

[My page references to the "keepandbeararms.com" site are the pdf
pages, which include the table of contents as "numbered" pages, not
the actual "text" of the article...the quotation is on page 66 of the
actual document.]