In Rurouni Kenshin, the Shinsengumi are introduced by Saitō Hajime, the former leader of its 3rd squad. Also, the major part of references to the Shinsengumi, both in the manga and in the anime series, are made by Saitō.
After Japan's political chaos in the 1850's, the country was divided along various lines of political opinion. Loyalists to the Emperor of Japan began a chain of murder and violence in Kyoto and because of this the Tokugawa Shogunate formed, in 1863, the Rōshigumi (浪士組 - Kyoto Defenders), a group of masterless samurai, whose formal mission was to protect Tokugawa Iemochi, the 14th shogun. However, Kiyokawa Hachiro (leader of the Rōshigumi) had a different goal: he wanted to gather rōnin (masterless samurai) to work with the supporters of the emperor. In response, thirteen members of the Rōshigumi became the thirteen founding members of the Shinsengumi.
In the start of their founding, the Shinsengumi were initially known as the Miburo (壬生浪), meaning ronin of Mibu (Mibu being the suburb where they were stationed). However, the reputation of being known as the ronin of Mibu became tarnished quite early on, and their nickname soon changed to Wolves of Mibu (壬生狼), a name that would be synonymous upon their ranks being formally now known as the Shinsengumi upon the second term of Aizu led Kyoto Shugoshoku, Matsudaira Katamori.
Okita Souji, Nagakura Shinpachi and Saitō Hajime were considered the strongest swordsmen of the group with Kondo Isami and Hijikata Toshizō acting as the lead commanders. The Shinsengumi later disbanded at the time Hijikata was killed in the Battle of Hakodate leaving them leaderless and thus the collapse of the Tokugawa and the surrender of the Bakufu army in 1869. Nagakura Shinpachi and Saitō Hajime were the only surviving head captains after the war. Saitō would later become a cop for the Meiji government and still carry the Shinsengumi's code Aku Soku Zan (Slay evil to death) with Nagakura writing stories of the Shinsengumi.
The Shinsengumi are firstly mentioned in chapter 48 of the manga (episode 28 of the anime series). Saitō Hajime makes his first appearance as a pharmacist selling a medicine to cure bruises and broken bones, a disguise that was often used by Shinsengumi spies. Later on, Saitō participates in several battles and in every one of them, he mentions the Shinsengumi motto: 'Aku Soku Zan - Slay Evil Immediately'.
Another Shinsengumi mention exists in Act 9 of the Manga series, with Udō Jin-e being mentioned to have sided with the Shinsengumi during the Bakumatsu.