Anime
The real-world OVA consists of Episodes 1, 21 (the "re-cap" episode, common to many anime series and used here as a means of giving some idea of what has happened in prior, unseen episodes), and 25 (the penultimate episode, and first part of a two-part finale) of this metafictional series. One episode is included in each of the three Genshiken DVDs released by Media Blasters in the United States.
As far as can be understood, Chihiro Enomoto is a freshman at the prestigious Rikkyoin High School (立橋院高校, Rikkyōin Kōkō?). The students of Rikkyoin are engaged in a year-long contest designed to determine which individuals will become the Student Council for the subsequent school year. At the start of the contest, lots are drawn (kujibiki roughly translates to "drawing straws" or "drawing lots"), and students are organized into groups according to the numbers they draw. These chance drawings also determine the positions and roles the students would take in the Student Council should the group they are a part of win the Kujibiki. (Chihiro, for example, would become Student Council Secretary.)
Competitions are staged between different groups, and because even one loss means that one's group is automatically eliminated from the Kujibiki, teamwork and cooperation is essential. The competitions appear to range from mental exercises to physical challenges, including a cooking contest, a swimming race, endurance tests against both extreme heat and cold, and an intense war game.
The side-story running alongside the main plot seems to involve the cold and calculating Student Council President, Ritsuko Kübel Kettenkrad. The viewer learns from flashbacks that Ritsuko and Chihiro were childhood friends. A pivotal and frequently-referenced scene in the series involves Ritsuko asking Chihiro to marry her someday, if she stops "being a crybaby". On the rare occasions she and Chihiro speak during the Kujibiki, she never brings up their childhood, but there is plenty of evidence to indicate that it is never far from her thoughts.
Read more about this topic: Kujibiki Unbalance