There are slides devoted to this topic: Lecture 7b.
Read the “Biography of John Atanasoff” from the History of Computers site, which provides an extensive description of Atanasoff’s life and work. Afterwards, visit “The ABC of John Atanasoff and Clifford Berry,” which covers the construction and operation of the ABC.
You can also look at the “Atanasoff-Berry Computer” page from the Computer History Museum for some information on the machine’s development and the decades-later patent quarrel with Sperry Rand and its ENIAC.
Watch a discussion with Jane Smiley, the author of The Man Who Invented the Computer. The eighty-minute video begins with an introduction from Gordon Bell, and a clip from a lecture delivered by Atanasoff in 1980, before turning to Smiley, her book, and Atanasoff. Despite the title of her work, she approached the history of the computer as a series of stories of people working independently on the same problem at the same time – her conversation thus covers Turing, Zuse and Eckert and Mauchly in addition to Atanasoff.
To see the man himself, check out a lecture presented by Atanasoff in 1980 (and excerpted for Smiley’s talk). Atanasoff gives a 75-minute slide presentation on his life and the “forces leading up to” the development of the ABC. The slides (not necessary for understanding the lecture) are not easily visible.
The Atanasoff-Berry Computer in Operation,” in which a demonstrator solves a set of equations on the ABC. Although dry, it is clear and has a great deal of information. If nothing else, you can appreciate the hairstyle of the demonstrator.
IEEE: “Advent of Electronic Digital Computing,” John Atanasoff: This article, written by Atanasoff, covers his early interest in logarithms, the base-2 system, the mathematics behind the computer he designed, the reasoning behind his decision-making processes, and the design and construction of the ABC. He also covers financial and patent issues surrounding the ABC, Mauchly’s visit, his later work in computers, and a good deal of information on the Honeywell v. Sperry Rand case. Engagingly written, it does suffer from a few large sections of complex mathematics–although these can be skipped without losing any understanding.
IEEE: “What Does it Mean to be the First Computer?” Michael Williams: In this short speech, the author answers the question of which computer was the first computer…by saying that the claim of “being first,” in the history of technology field, is not historically reliable. Williams first cites the Napier and his logarithms as an example of the vexing problem of accurate attribution. He then goes on to provide a brief history of computers, from the Difference Engine to the EDSAC, any of which could be – and are – considered the first computer. But the assertion that any computer was the first computer, argues Williams, is often a matter of national or institutional pride that would not hold up under historical investigation.
Campbell-Kelly and Aspray, Computer: A History of the Information Machine, 73-74