Internet technology has removed many of the traditional barriers to publishing, leading to a proliferation of new online publishers, many of whom use the gold open access model, a model where the contributing authors pay the costs associated with publishing and the content is then freely accessible online. Many open access publishers are legitimate, and even quite prestigious, but others have found a way to exploit the gold model, usually in the form of predatory open access journals.
Predatory open access journals are probably the most common form of predatory publishing encountered today. They can be defined as publications or publishers who "unprofessionally exploit the gold open-access model for their own profit. That is to say, they operate as scholarly vanity presses and publish articles in exchange for the author fee. They are characterized by various level of deception and lack of transparency in their operations. For example, some publishers may misrepresent their location, stating New York instead of Nigeria, or they may claim a stringent peer-review where none really exists."
How it works: an article is submitted and is quickly accepted for publication. Despite assurances of a traditional editorial and review process, the article receives very little copyediting, if any, and is rushed to publication. The author(s) never receives any notes, comments, or editing requests that would typically come from a peer-review process. At some point in the process, the author(s) is presented with a substantial and often unexpected invoice for the costs associated with the publication and review of the paper.
Abuse of the gold open access model is probably the most common form of predatory publishing encounter today, but it isn't the only way in which scholars and the peer review process can be taken advantage of.
How it works: an author submits a paper for presentation at a conference. The paper is accepted, and at some point in the process the author is asked to submit a (usually high) fee for registering/presenting. In some cases, there is an actual event, but in many cases, the conference is "delayed" or not actually held. The common theme is that these conferences all charge substantial fees for registering/presenting/attending, and the acceptance guidelines are lax to nonexistent. Click here to read the story of a team of MIT graduate students who had a randomly-generated (i.e. nonsense) computer science paper accepted for presentation at a conference.
In this model, it's not always the authors and presenters who are the targets. Some things that are advertised as conferences are actually outright scams designed to trick people into paying registration and attendance fees for nonexistent events.
How it works: an author submits a book chapter, and the chapter is published (usually with minimal/no editing) in a book or other print publication surrounded by public domain material, reprints from other publications, and other "filler." The publisher then targets libraries with collection development policies which indicate that they collection heavily or exhaustively in the relevant subject area(s) in hopes of selling the books at inflated prices. The author may also find that their work gets reprinted again and again in other publications without their permission or knowledge. Click here to read a story from a University of Chicago librarian who encountered a publication that allegedly fell into this category.