“Buy one and get one free” is a familiar promotion by retailers to move product. “Buy One—Get One Free” has been cited in print since at least 1908.
 
“BOGOF” has been cited since 1963 and “BOGO” since 1966, but the terms became popular in the mid-1980s and early 1990s. “BOGO” has proved to be more popular than “BOGOF.”
 
The second item is often discounted, not “free.” “Other times the second product is available at half price,” a 1992 “What is BOGO?” newspaper article explained.
 
     
Wikipedia: Buy one, get one free
“Buy one, get one free”, or “Buy one, get one” is a common form of sales promotion. While rarely presented to customers in acronym form, this marketing technique is universally known in the marketing industry by the acronym BOGOF, or just BOGO, and it is regarded as one of the most effective forms of special offers for goods[citation needed].
 
Technique
Originally, “buy one get one free” was a sudden end-of-season or stock clearance method used by shops who were left with a large quantity of stock that they were looking to sell quickly. More recently it has become a popular, planned and considered marketing method.
 
Economist Alex Tabarrok has argued that the success of this promotion lies in the fact that the price actually takes into account the fact that two items are being sold. The price of “one” is somewhat nominal and is typically raised when used as part of a buy one get one free deal. Whilst the cost per item is proportionately cheaper than if bought on its own, it is not actually half price.
 
Buy one get one free is a popular sales technique because it can be used legally at any time, unlike many other offers. For example a shop cannot claim an item is “on sale” or is discounted unless it has been available for sale at the previous, higher price for a certain period of time.
 
(Oxford English Dictionary)
BOGOF, n.
Brit.
[Acronym < the initial letters of the advertising slogan

buy one get one free.]
‘Buy one get one free’: a retail offer whereby a customer who purchases a particular item receives another such free of charge; an item obtained in this way.
1985 Progressive Grocer June 91 A recent buy-one, get-one-free (BOGOF) promotion.
1997 Scotsman (Electronic ed.) 21 Dec., When a friend who was ill received a pot plant from her brother, she said: ‘What a lovely poinsettia’. He replied: ‘It’s not a poinsettia, it’s a BOGOF—Buy One Get One Free.’
 
Google News Archive
25 June 1908, Pittsburg (PA) Press, pg. 10, col. 2 ad:
Buy One—Get One FREE
(Kaufmann’s “The Big Store”—ed.)
 
28 July 1911, Grand Rapids (MI) Press, pg. 1 ad:
BUY ONE AND GET ONE FREE
(Schrouder’s Central Drug Store—ed.)
   
11 July 1915, Tulsa (OK) World, sec. 2, pg. 6 ad:
BUY ONE AND GET ONE FREE
(Tulsa Garment Factory—ed.)
 
Google News Archive
15 November 1920, Rock Hill (SC) Evening Herald, pg. 5 ad:
BUY ONE AND
GET ONE FREE
(S. W. Plyler—ed.)
 
22 February 1963, Dallas (TX) Morning News, sec. 3, pg. 2 ad:
B.O.G.O.F.*
*BUY ONE…GET ONE FREE!
(Floral Art Center—ed.)
   
Google Books
How to Plan and Execute the Marketing Campaign;
Strategies for research, budget, copy, media, merchandising, and market testing, plus an actual marketing campaign document and 42 classic case histories in modern marketing
By Craig S. Rice
Chicago, IL: Dartnell
1966
Pg. 13:
The promotion was a BOGO (Buy One Get One—Free), or two six-packs for 51 cents.
       
Google Books
Going for it!:
How to succeed as an entrepreneur
By Victor Kiam
New York, NY: Fontana/Collins
1986
Pg. 255:
I thought a lot of customers would take advantage of the BOGOF (Buy one, get one free) promotion to try something else in our range.
 
Google Books
Local Store Marketing for Restaurants
By Jack Bernstein
Los Angeles, CA: JB&ME Advertising
1991
Pg. 58:
The following is a list of the most common forms: 1. Buy-One-Get-One Free (BOGO)...
   
Google News Archive
31 May 1992, The Robesonian (Lumberton, NC), “Job search sees highs and lows,” Business, pg. 1D, col. 6:
And then there were the cuts: He cut back on socializing, he cuts his own grass instead of paying a college student $60 a month to do it, he cuts out newspaper coupons for bargains and he cuts costs by BOGO-ing—his term for buy-one, get-one free supermarket specials.
 
Google News Archive
11 November 1992, Florence (AL) TimesDaily, “Bargain hunters scout stores for new deals” by Martin Sloane, pg. 1C, col. 2:
If you shop at the Farm Fresh supermarket in Virginia, you probably know what a “BOGO” sale is.
 
If you live in Princeton, Ill., you may have shopped in a new grocery store called BOGO’s. If you are a smart shopper who enjoys a bargain, then you defnitiely look for BOGOs.
 
What is BOGO?
 
The letters literally stand for “buy one, get one.” What do you get? Well, in many cases if you buy one product, you get a second for free. Other times the second product is available at half price.
   
The Independent (London)
Employee shares find ready takers
BRIAN FRIEDMAN
Sunday, 13 March 1994
(...)
Possibly the most innovative use of the profit-sharing scheme is the splendidly entitled BOGOF scheme. BOGOF stands for Buy One, Get One Free and is sometimes more elegantly referred to as a matching offer scheme.
 
A well tried and tested retailing concept, Buy One, Get One Free is attractive to employers who want to encourage their employees to buy shares in the company, albeit on favourable terms.